Find the second derivative (y") of the given function: 6. y 2-e -6e* +12e-e" (2-e*)" 6e* (2+e*) (2-e) 6e (1-e*) (2-e*) 12e2-6e" +12e2 (2-e*)4 x

Q: A A A A A A A A A A AA A A A A A A A A A A A A A A A AAA 6. What is the sum of the series TC + ... +…

A:

Q: Find dy/dx. x = Vt y = 9-t %3D dy dx

A:

Q: Vx² -9 What trigonometric substitution should be used to evaluate ? x2 A x=3 sece В x=3 tane C) None…

A:

Q: What is dy/dx for va+y+ Vay = 6?

A: Given problem:- What is dy/dx for √(x + y) + √(xy) = 6 ?

Q: Find the series' radius of convergence. n! Σ 5-10 - 15...- -5n n= 1

A: We have to find the radius of convergence.

Q: Find div F and curl F if F(x, y, z) = 13y'z4i – 16x4z10j – 3xy'k. - - div F= curl F=

A:

Q: Find V x (V x F) if F(x, y, z) = 6xyj+2xyz k. V × (V × F)

A:

Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, y, - 2z) across the…

A:

Q: 0y-25 +y= 2メ+3 %3D

A:

Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

A:

Q: Find V. (F x G), if F(x, y, z) = 3xi +j+ 10yk and G(x, y, z) = xi + yj – zk. - V. (F x G) =

A:

Q: dr Vr +3 5.

A:

Q: 4) Compare your answers

A: answer is in next step

Q: メーャゴ+2x)dメ+でyalyo

A: answer is in next step .please give a like

Q: 21 Given 3x7 +8x5 - , determine, y" O 630x4 + 480x² + 126 5x4 O 840x3 + 360x 504 - 504 O 2520x3 +…

A:

Q: dy Given the equation below, find dæ - 51a" + 7a"y + y10 = - 43 dy 172 (15 – 1422y) 29. dæ Now, find…

A:

Q: If f(x) = [ V19+ t² dt , find f'(3)

A:

Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (5, -5)

A: The objective of the question is evaluate the definite integral.

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: The partial derivative of f(x, y) = e"y – 2x – 4y + 3 with respect to x is O ye"V – 2 af af ery + y…

A:

Q: as (x*ty3) dx -2メydy =0 a.) prove if the given DE is exact or non -exact - Given DE b.) Find its…

A:

Q: Solve

A:

Q: 2. sin 2wcos 2wchw

A:

Q: 1. The resultant of two forces has a magnitude of 55 N in the southeast direction. What is the…

A:

Q: Find div F and curl F if F(x, y, z) = 4y³z'i – 11a"z°j – 4xy°k. - -

A:

Q: Find the average value of the function over the indicated interval.   ​(B) Graph the function and…

A: To find the average value of the function,      fA=1b-a∫abf(x)dxWe have, f(x)=500-90x, a=0, b=2

Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) to find k(t). 13 r(t) = 3 cos(3t)i+3 sin(3t)j + tk…

A:

Q: Find an equation of the tangent plane to the given surface z = x sin(x + y) at the point (-1, 1, 0).

A: Given,  z=x sin(x+y) ⇒x sin(x+y)-z=0 Let f(x,y,z)=x sin(x+y)-z Recall: The equation of the tangent…

Q: 3. For the given differential equation xy' – 4y = x*e* a) Find P(x) and Q(x) functions of a FOLDE.…

A:

Q: y = (sinh(@)) Solve for y'. Express your answer by factoring out a common facto

A: First I have taken the log on both side to the given function and then differentiating it with…

Q: For the given function find dy/dx. x- y' | = x + 2 y+ x2 1- x-3y-4x 3x2 + y + 2 y' 1- x + 3y - 4x y…

A: x-y3y+x2=x+2

Q: Determine wnetner the function Isa linear transrormation. T: R2 - R³, T(x, y) = (x², 3xy, 2y²)…

A:

Q: Determine the area of the region between the x-axis and the graph of the curv -1 from x- 0 to x- 4.…

A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

Q: (x^2+y^2-3)dx-2xydy=0 Prove the given DE is exact, and find general solution

A:

Q: EXAMPLE 3 Evaluate the following integral. VI- 4.r2 SOLUTION Let u = 1 - 4x². Then du %3D , SO xdx =…

A: We can solve as follows

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i + 11 sin(t)j +…

A:

Q: y = [log(arc cot r3)]cosh

A:

Q: ex-e-x b. Find the inverse function of f (x)

A:

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: Find all the first and second partial derivatives of the function f(r, y) = x°y – 3y“. %3D

A: Given :f(x,y)=x2y-3y4To find : All the first and second partial derivatives of the function

Q: Find V (V × F), if F(r, y, z) = 7e"i+6xe"j – 2ev²k. V· (V × F) =|0

A: We have to find ∇.∇×F→

Q: dr a 2 1 +3

A:

Q: Find the Maclaurin series for f(r) using the definition of a Maclaurin series. [Assume that has a…

A:

Q: Use the formula k(t) |r(t) × r"(t)|| x r" (t)|| to find «(t). ||r(t)||° r(t) = ti+ t5j «(t)

A: To find k(t).

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A:

Q: Find sin 0. 4 e in quadrant IV cot 0 = sin 0 = (Simplify your answer, including any radicals. Use…

A:

Q: 422+3r-2 Given z+1 determine y" 18 (z+1) (z+1) 2 (z+1) 10 (z+1)

A:

Q: Find y': y arcsin Oy =-- %3D Oy = - zV-9 %3D Oy = %3D zV-9 %3D -69

A:

Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

A:

Q: Determine the lowest positive root of f (x) = 8 sin(x)e–x − 1:        a.  Graphically.        b.…

A: The given function,     f(x)=8sin(x)e-x-1