Can i get help with those 30 questions ? MATH 280 calculus I .

NG beginning. Goals & stand Aligned with 2 Question 1 10 Points VI Attempts 3 attempts left A research lab grows a type of bacterium in culture in a circular region. The radius of the circle, measured in centimeters, is given by r(1) =5 - . where t is time measured in hours passed since a circle of a 1cm radius of the bacterium was put into the culture. Grading Express the area, A () , of the bacteria as a function of time, and find the approximate area of the bacterial culture in 4 hours. Maximum A A(t ) = 1 ( 5- 6 and Area after 4 hours = 14.72, cm 1 2 + 3 B A(t) = 2n(5- 6 72 + 3 and Area after 4 hours = 29.43, cm2 A(1) = 1 5 - 6 72 + 3 and Area after 4 hours = 68.93, cm- D A(1) = 27 5 - 6 2 1 2 + and Area after 4 hours = 137.86, cm Question 2 10 Points A minivan was purchased for $32,000. If the value of the minivan depreciates by $1,700 per year, find a linear function that models the value V of the car after t years. Use the function and find the value of the car after 5 years. (A V(t) = -1,700t + 32,000; value after 5 years = $23,500Question 9 10 Points Consider the function f (x) shown in the following image: Evaluate lim f(x). =0 \f\f\fQuestion 12 10 Points 2x- + 3x + 1 Find the intervals over which the function f (x) = is continuous. x- - 5x ( - 00, 5) and (5, co ) B (- 00, 0) and (0, co ) c (- 00, 0), (0, 5) and (5, 00 ) ( - 00, - 5), (-5, 0) , and (0, co )Question 13 10 Points tan kx Find a non-zero value for the constant k that makes the function f (x) = X continuous at x =0. x20 5x + 3, A D - 310 Points Question 14 Determine the value of 6 >0 for which lim (3x- - 1) =47 . 1+4 m A 6 = max { - 4-, 16- - 4+ 16+ } B 6 = min { - 4+ 16- - 4- 16+ 3 E 6 = max {4-, / 16- 4+ 16+ D 6 = min {4- , / 16- - 4+ 1 16+ w |m 3Question 15 10 Points Determine the value of 6 > 0 for which lim = 00 . x-2 (x-2)2 A 6= M B 6= M 6= /M D 6=MQuestion 16 10 Points A store determines that the daily profit on pens obtained by charging s dollars per penis P(s) = 10524 755 5. If the store currently charges 50 cents for a pen, find the rate of change of profit. $30 Question 17 10 Points A ball is dropped from the top of a building that is 15 m high. The position of the ball after t seconds is given by the equation s (1) = - 4.9-+ 15. Find the instantaneous acceleration of the ball after t seconds. A -4.9; m/s- B -9.8; m/$2 -9.8t; m/$2 D -4.9t; m/$2Question 2 10 Points A minivan was purchased for $32,000. If the value of the minivan depreciates by $1,700 per year. find a linear function that models the value V of the car after t years. Use the function and find the value of the car after 5 years. @ V{t) = 1,700t + 32,000; value after 5 years = $23,500 Vt) =-1,700 + 32,000; value after 5 years = $30,300 V(t) = 1,700 + 32,000; value after 5 years = $33,700 @ V(t) = 1,700t + 32,000; value after 5 years = $40,500 \fQuestion 19 10 Points The price p (in dollars) and the demand x for an item is given by the price-demand function p(x) = 15 0.0015x. Find the marginal revenue at x=1,000. Question 20 10 Points Find the equation of the tangent line to f (x) =3csex + xsinx at x = A y=x-3 B y=x+3+ 2 c y=x+3 D y=x+3-Question 21 10 Points A bag of sand hanging from a vertical spring is in simple harmonic motion as given by the position function s (t) = - sin(-+ 6 where t is measured in seconds and s is in inches. Find the velocity of the spring at = 2 5. A inch/s 4 B - inch/s 4 C inch/s 4 D -inch/s 2\fQuestion 23 10 Points The volume of a right circular cylinder of radius x and height y is given by v=xx y. Suppose that the volume of the cylinder is dy constant at 250xem. Find when x = 5 and y = 10. dx A - 100 B 4 4 D 250\f\fQuestion 26 10 Points If f (x) =/ 1+ 8x , find f '(a) for a=3 and the equation of the tangent line to f (x) at x=a. 5x - 13 A f ( a ) = ; equation of the tangent line is y = 4 - 4x + 13 B) f ' ( a ) = - ; equation of the tangent line is y = 5 4x + 13 f (a)= Uil A ; equation of the tangent line is y = 5 - 5x - 13 D - = (0). J ; equation of the tangent line is y = 4 4Question 27 10 Points The position of a moving particle as a function of time is given by s (() = - 23 - t+ 1, where s is in meters and t is in seconds. Find 3 the time at which the particle is at rest and the acceleration of the particle at = 3 5. A Time at which the particle is at rest =2 s ; acceleration of the particle =2 m/s- B Time at which the particle is at rest =1 s ; acceleration of the particle =6m/s C Time at which the particle is at rest =2 s ; acceleration of the particle =1 m/s- D Time at which the particle is at rest =3 s ; acceleration of the particle =3 m/sQuestion 4 10 Points m A pendulum moving in simple harmonic motion is modelled by the function .s'(:] = 5cos( T) .where s is measured in inches and t is measured in seconds. Determine the first time when the distance moved is 4 inches. @ 0.82s 265 23 Questions Filter (30) v 5 Question 28 10 Points A car moves on a straight road. The car's position at time : is given by s () =t + sint, where s is in meters and t is in seconds. Find the acceleration at t = -; s. 4 A -; m/$2 B ; m/s- 2 : m/ $2 2 D 1; m/$2\f\fQuestion 4 10 Points e A pendulum moving in simple harmonic motion is modelled by the function .'(.r] = 5cos( T) . where s is measured in inches and t is measured in seconds. Determine the first time when the distance moved is 4 inches. \fQuestion 6 10 Points Estimate the slope of the tangent line to ;"(.t] =xatx=2 by finding the slope of the secant line through (2, f(2)) and (2.001, f(2.001)). @ 0.012 4.002 @ 12.000 @ 16.012 Question 7 10 Points The following image shows the graph of the function (x) =4/ 4x2; y a5 1 15 2 Find the area between the x-axis and the graph of f(x) over the interval of [ 2. 2] using the shaded squares. (A) 6.27 square units Find the area between the x-axis and the graph of f (x) over the interval of [ 2, 2] using the shaded squares. @ 6.27 square units 7.5 square units 12.57 square units @ 8 square units \f