Differentiation Questions and Answers

Find y for y y x defined implicitly by 5y2 8x4 3 0 and evaluate y at x y 1 1 11x3 5y y l 1 1 11x2 5y2 1 1 11 16x3 y 16 y 1 1 16 5y y 162 1 1 16

Given the region bounded by the graphs of y In x y 0 and x e find the following Round your answers to three decimal places a the area of the region 1 718 X b the volume of the solid generated by revolving the region about the x axis 11 199 X c the volume of the solid generated by revolving the region about the y axis 6 283 X d the centroid of the region 1 859 0 581

tan u 5 12 3 2 c 2 a Determine the quadrant in which u 2 lies O Quadrant I O Quadrant II O Quadrant III O Quadrant IV

Write the function as a composition of two functions y 4x 7 8 For flg x g x

48 Given sine and is in Quadrant II find cote A B 413 C 4 D 3

34 A boat travels N 31 E for 65 miles and then N 59 W for 102 miles Find the distance of the boat from its starting point A 37 miles B 79 miles C 121 miles D 167 miles

20 The reference angle of 292 is A 32 B 22 C 58 D 68

2 Evaluate the expression cos 240 without using your calculator A 3 B 3 D 1 2

Find dy dx dy d y dx and given y 6x 3 6y dx 3 y 3 Note Answers with y are not allowed d y dx 9 y 3 V

dy dx y ln x 8x y 8 dy dx Find where

Use implicit differentiation to find y 3x 4y 6x dy dx dy dx

Find dy dx dy d y dx and given y 6x3 6y dx Note Answers with y are not allowed d y dr

7 f x has only one discontinuity lim f x 1 f 1 4 lim f x 1

Find the slope of the tangent line to the curve 2x 4xy 4y 56 at the point 2 2

If f y tan 6y find f y Use exact values f y 1 1 36y

If x y 10 and y 9 49 find y 9 by implicit differentiation

Slides die st a c SPEEL 1 Evaluate 2 x dx x 2 8 8 tan tan 2x 2x 2 1 X 2x 2x 2 1 X C 2 17 c C b d 8 tan x 2 1 4 tan 2x x 2 52 x 2x 2x 2

Take the derivative of each function using the chain rule f g x f g x g x 1 y 2 f x 1 2 y x 4x 6 3 f x x 5x 1 4 y x 2x 5 5 f x x 1 2 1 6 y 2 1

Differentiate the following function r t 6te 5tln t tsin t

Consider a portfolio problem with n assets e g stocks over some fixed period The rate of return for asset i is defined to be the change in asset s price over the period For instance if the price changes from p to prew the rate of return is phew Pi P The rate of return for each asset i i 1 N is given by a random variable R with mean r E R Furthermore the covariance of R and R is equal to E E R r R r Denote the total budget for investment by B which we assume is equal to one for simplicity Let RT be the total return on investment In other words RT R I where I is the initial investment in asset i i 1 n A good investment strategy needs to balance the trade off between the total return and the risk measured by the variance of RT i e the higher the variance of Ry is the riskier the strategy is a Set up an appropriate convex optimization problem for maximizing the expected total return E R subject to a constraint that the variance of Rr does not exceed o2 b Set up an appropriate convex optimization problem for minimizing the variance of the total return subject to a constraint that the expected total return is at least Rmin

of experience po Calc I Chapter 3 ntly in the direction of yo RK ON EACH PROBLE

Spr23 Calc I Chap Go confidently in the directio SHOW WORK ON EACH PR 3 Determine and compl

mplify the trig expression secx tan x cos x sinx

K Determine the eq The equation of t Type an equatio

Factor the trinomial x 12x 35 Select the correct choice 12x 35

Write two steps of the forward and backward Euler method for the following equatio y 2y 1 y 0 1 h 0 1

w 8 w 6 w 8 w 6 Simplify your answ

2 Use proof by induction to show n 2n 3 for integer values n 3

Find a complex number z that satisfies the following equation 4 2i z 5 2i 2z

Determine the slope of the line 9 6 and 9 10 Select the correct choice belov

Determine the slope of the lin 3 2 and 8 6

For the function y f x x 4x 1 x 2 find 1 3 200 8 df 1 dy y 3

Find the curvature K of the curve 2 k k 2 K r t ti t j

Let f x x 2x T Then f x is f 4 is f z is and f 4 is

Let f and g be differentiable fun f 2 6 g 2 9 Let h be the new function define What is the formula for h x

rk 2 1 Elementary Deriv 0 15 answered h 10 of the tangent line to the parabola y

0 15 answered erivative of 6476

re 0716 0 15 answered Question 13 4 3 4 3 2 1 2 3 4

0 16 0 15 answered Question 6 x 2 S 8 Elemen 6 T 3 find

0 16 0 15 answered uestion 1 f f x x f g x AKAR 10 then f x 4r then g x

1 Protozoan population A population of protozoa develops with a constant relative growth rate of 0 7944 per member per day On day zero the population consists of two members Find the population size after six days

31 Infectious disease outbreak size In Example 13 we used the equation pe 9A 1 A to determine the rate of increase of the outbreak size A with respect to the transmissibility q Use this same equation to find the rate of change of A with respect to p the fraction of the population that is initially susceptible to infection

77 80 Use implicit differentiation to find an equation of the tangent line to the curve at the given point 77 x xy y 3 1 1 ellipse

53 Find the 50th derivative of y cos 2x

24 Kerwin pulls with a force of 25 Newtons on the handle of a wagon to move it along level ground If the 61 handle makes an angle of 35 with the horizontal how much work would Kerwin do by pulling the wagon 150 meters Round your answer to two decimal places 629

5 24 then 3 Estimate your answer to two decimal places

of ever zero Find the derivative of each of the following functions 8 a f t 2 b y x 7x c y 2x 6x 1 8

5 A relative maximum occurs at 1 3 8

Suppose is a differentiable function of x and y and g r s f 3r s s 4r Use the table of values below to calculate 945 7 and g 5 9 5 7 s 5 7 8 29 5 7 f 1 5 9 5 1 4 3 B 6

Evaluate the definite integral Lole 2 x 1 ex 2x 8 dx