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Straighterline MAT 250 Graded Midterm Exam

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9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 1/18 MAT250_TW_V3 | Chapter 8: Curve Sketching (877) 787-8375 HELP CENTER Question 1 Correct 5.... 00 points out of 5.00 Question 2 Correct 5.00 points out of 5.00 Started on Sunday, September 5, 2021, 2:04 AM State Finished Completed on Sunday, September 5, 2021, 3:47 AM Time taken 1 hour 43 mins Grade 160.00 out of 200.00 (80%) Suppose a particle’s position is given by , where is measured in seconds and is given in centimeters. What is the velocity of the particle when ? Select one: a. b. c. d. On which interval is increasing? Select one: a. b. and c. d. f(t) = t4 t f(t) t = 3 v = 81 cm/sec v = 108 cm/sec v = 324 cm/sec v = 1728 cm/sec f  (x) = x 3 −3x2 − 9x + 1 (−1, 3) (−∞, −1) (3, ∞) (−∞, 1) (1, ∞)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 2/18 Question 3 Incorrect 0.00 points out of 5.00 Question 4 Correct 5.00 points out of 5.00 Question 5 Correct 5.00 points out of 5.00 Consider the function Is continuous at ? Select one: a. Yes, is continuous at . b. No, f(x) is not continuous at x = 0. c. There is not enough information. Use the linear approximation method to estimate the value of \( \ln(2.7^2) \) in terms of \( e \). Select one: a. \( \displaystyle \frac{5.4}{e} \) b. \( \displaystyle \frac{5.4+e}{e} \) c. \( 4- \displaystyle\frac{5.4}{e} \) d. \( \displaystyle \frac{2e-5.4}{e^2} \) What is the slope of the line tangent to the curve \( x^2y^2 = 1 \) at the point \( (1, 1) \)? Select one: a. \(0\) b. \(1\) c. The slope is unde¦ned. d. \(-1\) f(x) = x3 + x x f(x) x = 0 f(x) x = 09/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 3/18 Question 6 Correct 5.00 points out of 5.00 Question 7 Correct 5.00 points out of 5.00 Question 8 Correct 5.00 points out of 5.00 What is the derivative of the function \( f(x) = x^3 +2e^{2x} \)? Select one: a. \( 3x^2+4e^{2x} \) b. \( 3x^2+2e^{2x} \) c. \( 3x^2+2e^2 \) d. \( 3x^2+2e^x \) Use implicit differentiation to ¦nd an equation of the line tangent to the curve \( x^2 + y^2 = 10 \) at the point \( (3, 1) \). Select one: a. \(y=-x\) b. \(y=x\) c. \(y=-3x+10\) d. \(y=3x-8\) A ball is rolling along the \( x \)-axis. Its position (in feet) at time \( x \) (in seconds) is given by \( f(x) = 2\sqrt{x} \). Find its instantaneous rate of change when \( x=9 \) seconds. Select one: a. \( 6 \, \hbox{ft/sec} \) b. \( \displaystyle\frac{1}{12} \, \hbox{ft/sec} \) c. \( \displaystyle\frac{1}{3}\, \hbox{ft/sec} \) d. \( \displaystyle\frac{2}{3} \, \hbox{ft/sec} \)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 4/18 Question 9 Correct 5.00 points out of 5.00 Sketch the parabola of equation \( y=x^2-6x+9 \), and indicate its vertex. Select one: a. b. c. d.9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 5/18 Question 10 Correct 5.00 points out of 5.00 Question 11 Incorrect 0.00 points out of 5.00 What is the derivative of the function \( f(x) = -\, \displaystyle \frac{1}{4x^6} \)? Select one: a. \( \displaystyle \frac{3}{2x^7} \) b. \( -\, \displaystyle \frac{3}{2x^5} \) c. \( \displaystyle \frac{3}{2x^5} \) d. \( -\, \displaystyle \frac{3}{2x^7} \) If \( \displaystyle\frac{dy}{dx}= 0 \) for a given value of \( x \), then the line tangent to the curve \( y = f (x) \) at that value is horizontal. Select one: a. true b. false9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 6/18 Question 12 Correct 5.00 points out of 5.00 Question 13 Correct 5.00 points out of 5.00 What is the limit of the function in the graph at \( x=4 \)? Select one: a. \( \infty \) b. \( 6 \) c. The limit does not exist. d. \( 2 \) Consider the function \( y=x^2 + x + 9 \). What is the equation of the tangent line at \( x = 2 \)? Select one: a. \(y=-5x+5\) b. \(y=5x+5\) c. \(y=5x-5\) d. \(y=-5x-5\)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 7/18 Question 14 Correct 5.00 points out of 5.00 Question 15 Correct 5.00 points out of 5.00 Question 16 Correct 5.00 points out of 5.00 The position of a car at time \( t \) is given by the function \( p (t) = t^2 + 4t − 17 \). Where will the car be when it moves at a velocity of \(10\)? Assume \( t \geq 0 \). Select one: a. \(-4\) b. \(4\) c. \(3\) d. \(-3\) A man \(6\) feet tall is walking toward a building at the rate of \(5\;\hbox{ft/sec}\). If there is a light on the ground \(50\;\hbox{ft}\) from the building, how fast is the man’s shadow on the building growing shorter when he is \(30\;\hbox{ft}\) from the building? Select one: a. \( - \displaystyle\frac{5}{6} \;\hbox{ft/sec} \) b. \( -\displaystyle \frac{65}{6}\;\hbox{ft/sec} \) c. \( -\displaystyle \frac{15}{4}\;\hbox{ft/sec} \) d. \( -\displaystyle \frac{45}{4}\;\hbox{ft/sec} \) Compute the derivative of the function \( f(x) = \displaystyle \frac{x-x^2}{3x+5} \). Select one: a. \( \displaystyle \frac{(1-2x)(3x+5)\,+\,3(x-x^2)}{(3x+5)^2} \) b. \( \displaystyle \frac{(1-2x)(3x+5)\,-\,3(x-x^2)}{(3x+5)^2} \) c. \( \displaystyle \frac{1-2x}{(3x+5)^2} \) d. \( \displaystyle \frac{1-2x}{3} \)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 8/18 Question 17 Correct 5.00 points out of 5.00 Question 18 Correct 5.00 points out of 5.00 Given \( xy = 5 \), ¦nd \( \displaystyle\frac{dy }{dx} \) by implicit differentiation. Select one: a. \( \displaystyle\frac{y}{x} \) b. \( \displaystyle\frac{x}{y} \) c. \( - \displaystyle\frac{y}{x} \) d. \(0\) The given region is the combination of a semicircle with radius \( 2 \) cm and a right isosceles triangle with base length \( 4 \) cm. Find the area of the given region using the formula for the area of a circle, \( A = \pi r^2 \) where \( r \) is the circle's radius, and the formula for the area of a triangle, \( A = \displaystyle\frac{bh}{2} \) where \( b \) and \( h \) are the lengths of the triangle's base and height, respectively. Remember, a semicircle's area is one half the area of the circle with the same radius. Select one: a. \( 8+2π\,\,cm^2 \) b. \( 16+4π\,\,cm^2 \) c. \( 16+2π\,\,cm^2 \) d. \( 8+4π\,\,cm^2 \) e. None of the above9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 9/18 Question 19 Correct 5.00 points out of 5.00 Question 20 Correct 5.00 points out of 5.00 Question 21 Correct 5.00 points out of 5.00 Differentiate the function \( f(x) = 2x \). Select one: a. \(2x\) b. \(0\) c. \(x^2\) d. \(2\) Evaluate the following as true or false: If \( f ''(x) < 0 \) and \( f '(x) = 0 \) at the point \( (x, f(x)) \), then the point must be a relative maximum. Select one: True False Given \( xy = y^3 \), ¦nd \( \displaystyle\frac{dy}{dx} \) by implicit differentiation. Select one: a. \( \displaystyle\frac{1}{2y} \) b. \( \displaystyle\frac{y}{3y^2-x} \) c. \( \displaystyle \frac{y}{x-3y^2} \) d. \(2y\)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 10/18 Question 22 Correct 5.00 points out of 5.00 Question 23 Incorrect 0.00 points out of 5.00 Question 24 Correct 5.00 points out of 5.00 Let \( f'(x) = 3x^2+4x \) de¦ne the instantaneous rate of change (in \ (\hbox{ft/min}\)) of a car moving along the \(x\)-axis. What is the instantaneous rate of change at time \(1 \, \hbox{min}\)? Select one: a. \(10 \, \hbox{ft/min}\) b. \(7 \, \hbox{ft/min}\) c. \(3 \, \hbox{ft/min}\) d. \(4 \, \hbox{ft/min}\) A man \(6\) feet tall walks at a rate of \(5\;\hbox{ft/sec}\) away from a light that is \(15\) feet above the ground. When he is \(10\) feet from the base of the light, at what rate is the length of his shadow changing? Select one: a. \( \displaystyle \frac{25}{3}\;\hbox{ft/sec} \) b. \(\displaystyle \frac{5}{3}\;\hbox{ft/sec} \) c. \( \displaystyle \frac{10}{3}\;\hbox{ft/sec} \) d. \(\displaystyle \frac{5}{9}\;\hbox{ft/sec} \) Compute the derivative of the function \( f (x) = \sec x \). Select one: a. \(\cos x\) b. \(- \tan x \sec x\) c. \( \sin^2 x\) d. \( \tan x \sec x\)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 11/18 Question 25 Correct 5.00 points out of 5.00 Question 26 Incorrect 0.00 points out of 5.00 Question 27 Correct 5.00 points out of 5.00 Determine, if it exists, \( \displaystyle {\lim_{x→-2}}\,\,\frac{1+\frac{2}{x}}{x- \frac{4}{x}} \) Select one: a. \( \displaystyle \frac{1}{4} \) b. \( \displaystyle -\frac{1}{4} \) c. \( 1 \) d. The limit does not exist. What is the derivative of the function \( f (x) =\log _x 2 \)? Select one: a. \( -\displaystyle\frac{\ln 2}{x(\ln x)^2} \) b. \( \displaystyle\frac{2}{x} \) c. \( 2x \) d. \( \displaystyle\frac{\ln 2}{x(\ln x)^2} \) True or false? Let \(A\) be the area of a circle with radius \(r\) that is changing with respect to time. If \( \displaystyle\frac{dr}{dt} \) is constant, then \( \displaystyle\frac{dA}{dt} \) is also constant. Select one: True False9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 12/18 Question 28 Incorrect 0.00 points out of 5.00 Question 29 Correct 5.00 points out of 5.00 Question 30 Correct 5.00 points out of 5.00 Compute the derivative of the function \( f(x) = \tan(2x+1) \). Select one: a. \( \sec^2(2x+1)\) b. \(2 \sin^2(2x+1)\) c. \(-2 \sec^2(2x+1)\) d. \(2 \sec^2(2x+1)\) Determine \( \displaystyle\frac{d^{2}}{dx^2} [e^{3x}] \) Select one: a. \( 3e^{9x} \) b. \( 9e^{3x} \) c. \( 3e^{3x} \) d. \( 9x^2 e^{3x} \) Which of the following equations could be an equation of a vertical asymptote of \( y= \displaystyle \frac{x^2-2x}{x^2-6x+8} \) Select one: a. \( x=0 \) b. \( x=1 \) c. \( x=2 \) d. \( x=4 \)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 13/18 Question 31 Correct 5.00 points out of 5.00 Question 32 Incorrect 0.00 points out of 5.00 On Friday night, Ken drove one and a half hours at ¦fty-¦ve miles an hour to attend a concert in Austin. How far did he drive? Select one: a. \( 36.67 \) miles. b. \( 82.5 \) miles. c. \( 0.03 \) miles. d. \( 56.5 \) miles. Compute the derivative of the function \( f(x) = \cot(2x-1) \)? Select one: a. \( -2 \sin(2x-1) \) b. \( 2 \csc^2(2x-1) \) c. \( -2 \csc^2(2x-1) \) d. \( - \csc^2(2x-1) \)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 14/18 Question 33 Correct 5.00 points out of 5.00 Question 34 Correct 5.00 points out of 5.00 What is the limit of the function in the graph at \( x=4 \)? Select one: a. \( 6 \) b. \( 2 \) c. \( 4 \) d. The limit does not exist. Compute the derivative of the function \( f(x) = \displaystyle \frac{2x}{(3x^{2}+2)^{3/2}} \). Select one: a. \( -\, \displaystyle \frac{12x^{2}}{(3x^{2}+2)^{3}} \) b. \( \displaystyle \frac{2(3x^{2}+2)^{3/2}-18x^{2}(3x^{2}+2)^{1/2}} {(3x^{2}+2)^{3}} \) c. \( \displaystyle \frac{2(3x^{2}+2)^{3}+36x^{2}}{(3x^{2}+2)^{3}} \) d. \( \displaystyle \frac{2(3x^{2}+2)^3-36x^2(3x^{2}+2)^{1/2}}{(3x^{2}+2)^{3}} \)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 15/18 Question 35 Correct 5.00 points out of 5.00 Question 36 Incorrect 0.00 points out of 5.00 A particular rectangle has a length of \( 3 \) feet and a width of \( 2 \) feet. What is the area of the described rectangle? Select one: a. \( 3 \) square feet. b. \( 10 \) square feet. c. \( 5 \) square feet. d. \(6 \) square feet. What are the \( x- \)coordinates of the points of in§ection of \( f(x) = x(x-4)^3 \)? Select one: a. \( x=1 \) only b. \( x=2 \) only c. \( x=1 \) and \( x=4 \) d. \( x=2 \) and \( x=4 \)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 16/18 Question 37 Correct 5.00 points out of 5.00 What is the limit of the function in the graph at \( x=4 \)? Select one: a. \( 6 \) b. \( 4 \) c. \( 8 \) d. The limit does not exist.9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 17/18 Question 38 Incorrect 0.00 points out of 5.00 Question 39 Correct 5.00 points out of 5.00 If the graph of the derivative of \( f(x) \) is shown, at which \( x \)-coordinates would \( f(x) \) have a point of in§ection? Select one: a. \( x=q \) only b. \( x=q \) and \( x=s \) c. \( x=r \) and \( x=s \) d. \( x=p \) and \( x=s \) A body is thrown upward so that its height \( h \) at the end of \( t \) seconds is \( h=160t-16t^2 \) ft. Which of the following is its maximum height? Select one: a. \( 800 \) b. \( 400 \) c. \( 200 \) d. \( 600 \)9/5/2021 Graded Midterm Exam https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095564 18/18 Question 40 Correct 5.00 points out of 5.00 Compute the derivative of the function: \( f(x) = \bigg( \displaystyle \frac{x+1}{x-1} \bigg)^{5} \). Select one: a. \( 5 \bigg( \displaystyle \frac{x+1}{x-1} \bigg)^{4} \) b. \( 10x \displaystyle \frac{(x+1)^{4}}{(x-1)^{6}} \) c. \( -10 \displaystyle \frac{(x+1)^{4}}{(x-1)^{6}} \) d. \( 10 \displaystyle \frac{(x+1)^{4}}{(x-1)^{6}} \) Quiz navigation Show one page at a time Finish review 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Questions? Please contact our Student Advisors at (877) 787-8375, Live Chat, or create a Support Request Copyright © 2021 StraighterLine. Privacy Policy Terms of Use [Show More]

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