Calculus

Let rt=<6cos t,3sin t> , for 0 ≤ t ≤ 2 π a. Find the unit tangent vector at all points on the curve b. Find the principal unit normal vector at all points on the curve

Find all relative extrema of the function. Use a graphing utility to verify your result. If an answer does not exist, enter DNE. y=ln 4x-8x2 relative minimum x,y=square relative maximum x,y= =square

Determine whether the sequence converges or diverges. If it converges, find the limit. If an answer does not exist, enter l a_n=frac n32n+6 limlimits _nto ∈ fty a_n=square

Use implicit differentiation to find dy/dx , for y6=-frac 4y7+10x dy/dx = 1. Question Help: D Video Written Example Submit Question Jump to Answer

y=x2,z=0 , and y+18z=36. 3 ? ？ fx,y,z dz dy dz ? 3 0 36 ？ ? fx,y,z dz dz dy 0 3 0 36 ? ? fx,y,z dz dz dy ? 。 0 ? ? fx,y,z dz dy dz 0 0 3 ? 3 dy dz dz fx,y,z 3 0 ? ？ ? fx,y,z dy dz dz ? 7 0

Find the derivative of fx=4x2-6x+3cot x+2cos x. f'x=square

Find the absolute extrema if they exist, as well as all values of x where they occur, for the function fx=frac 8xx2+5 on the domain [-4,0]. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum is square , which occurs at x=square . Round the absolute maximum to two decimal places as need...

Given the equation below, find dy/dx . 51x10+8x85y+y9=60

Com A function f and a point P are given. Let 0 correspond to the direction of the directional derivative. Complete parts a. through e. fx,y=ln 1+5x2+4y2 F 1/4 ,- square root of 5 arctan -frac . s 5]+2 π Type your answer in radians. Type an exact answer in terms of x. Use a comma to separate answers as needed. What angles are associated with the ...

Homework Part 2 of 2 Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. limlimits _xto frac π 2-frac tan xfrac 142x- π Fow should the given fimit be evaldated? Select the correct choice below and, if necessary, m in the answer box to complete your choice. A. Use a trigonometric identity to rewrite the limit as lim . xto ...