Calculus

∈ t sin 3xcos xdx ∈ t sin 2xcos xsin xdx ∈ t 1-cos 2xcos xsin xdx

Find an equation of the tangent plane to the given surface at the specified point. 1 z=2x2+y2-5y,1,2,-4 2 z=ex-y,2,2,1

For each of the following, find f''x. 31. fx=frac x3-3x2-4x-12x 1

sumlimits _n=1 ∈ fty frac n8x6n531441n. Find the center and radius of convergence R. If it is infinite, type ''infinity" or ''inf''. Center a=0 Radius R=3 What is the interval of convergence? -3,3 Give your answer in help intervals.

The height of a rectangular box is 10 in. Its length increases at the rate of 2 in/sec; its width decreases at the rate of 4in/sec. When the length is 8 in. and the width is 6 in., the rate in cubic inches per second, at which the volume of the box is changing is A 200 B 80 C −80 D - 200 E −20

Find f'''1. fx=3x4-x2-2x Show your work here f'''1= + * overline square Find y'' . Use implicit differentiation and write the answer in terms of x and y. -x4=-3y5-9 Show your work here Hint: To add the nth root symbol square root of [square ]square , type "root" y''=

Use logarithmic differentiation to differentiate each function with respect to x. 1 y=2x2x 2 y=5x5x 3 y=3x3x 4 y=4xx4 5 y=3x4+43 square root of 5x3+1 y=x5+52 square root of 2x2+3 6 7 y=frac 3x4-253x3+42 8 y= square root of 3x2+13x4+13 9 y=frac square root of 2x3+3x4-33 10 y=2x2-53 square root of x2-2

Find the derivative of the function. y=2x2-4x+4e-6x Find the rule that should be used first in find The product rule should be used first. dy/dx =2x2-4x+4 d/dx e-6x+e-6x d/dx dy/dx =square

Exercise. Suppose the function px satisfies p-2=5,p'-2=1 , and p''x<0 for x values nearby -2. Task 1. Explain and demonstrate how to find the linearization Lx of px at x=-2. * Hide answer Lx=x+7 Task 2. Explain and demonstrate how to estimate the value of p-2.03 using this linearization. * Hide a...

Find the derivative implicitly. y2+3xy=4x3 dy/dx =frac 12x2-[?]yy+x