F(r, y) = (2xy³ +3)i+ (3x²y² + 2e²»)j is conservative by finding a potential function f for F, and use f to compute F. dr. where C is the curve given by 2t sin" 5tj r(t) = 2 sin' ti+ 10 for 0

Q: a2f дхду' a2f 2. (a) If f (x, y) = x tany + ye-2*, find and What do you notice? дхду (b) If f(x, y)…

A:

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

A:

Q: Let flx)= : Find the horizontal and vertical asympto tes. 2-ex

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

A:

Q: Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and…

A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex)…

A:

Q: aw aw = f(s³ + t²) and f'(x) = e*. Find and at əs Assume that w=f[s]

A:

Q: Find the directional derivative of f (x, y) = tan at P(-2,2) in the %3D direction of a = -i- j.

A: The function given is f(x,y)=tan-1yx. The directional derivative is to be found at (-2,2) along the…

Q: 20-21) What is the equation of the tangent line to y = x3 at x=2? A) y = x - 12 B) y = 12x C) y = x-…

A: Use derivative for finding the  equation of tangent line .

Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

A:

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

A:

Q: Q4: Find the derivative of the function at P, in the direction of A 2 1) f(x, y) = 2xy-3y², P.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: For the scalar function U = (1/r)sin^2(o), determine its directional derivative along the radial…

A:

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

A:

Q: What is the largest value of the function f (x,y) = x³y³ on the curve x4+ y^= 1? O 2-1/2 0 3√4 01…

A:

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: Use the given values to find (f-1)'(a). f( – 3) - 1, f'( – 3) - 2, а %— - 1 | (f-')'(a) = Preview…

A: Final answer is -(1/2)

Q: Hiw/ Find F'(x) 1 x, tanx if F(x) = X 2-if y= Sinx 3-Find y" (I)if yex) = Sec

A:

Q: Find f. f'(t) = 8 cos t + sec²t, -π/2 < t < π/2, f(π/3) = 2

A:

Q: tan x= Sin 2X

A: Given: y'+y tan x= sin2x

Q: Q6: A: If f(x,y)=ycos⁡x+xe^y.find f_x,f_y,f_xx,f_yy,f_xy B: Find the derivative of…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine order and degree * d'y d'y + cos dr? dr? 2 O 5 undefine- Not linear

A: The degree of a differential equation is the power of its highest derivatives.

Q: Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y =…

A:

Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

A:

Q: Let f(x, y, z) = x^2 + y^3 + z^5 and let u =. Find the directional derivative Du f(x, y, z).

A: The directional derivative Du​f(x,y,z) is 64/81​.Explanation:Step 1: To find the directional…

Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

A: