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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
mplify the trig expression secx tan x cos x sinx
K Determine the eq The equation of t Type an equatio
Calculus
Differentiation
K Determine the eq The equation of t Type an equatio
Factor the trinomial x 12x 35 Select the correct choice 12x 35
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
rk 2 1 Elementary Deriv 0 15 answered h 10 of the tangent line to the parabola y
0 15 answered erivative of 6476
Calculus
Differentiation
0 15 answered erivative of 6476
re 0716 0 15 answered Question 13 4 3 4 3 2 1 2 3 4
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
Evaluate the definite integral Lole 2 x 1 ex 2x 8 dx