Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: Calculate x sin(y)dxdy

A: On solving this we will get

Q: sin° xcos xdx x cos'

A: We will use substitution method to solve this definite integral.

Q: (-4)* 5k +1 k=1

A: We have to find if the series convergent or divergent.

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y= 0, y = 7+a*…

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Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P…

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Q: Evaluate the iterated integral. /8 3/y sin y dz dx dy Jo

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Q: Evaluate the line integral / (x +8y)dx + (5x – 4y)dy along the - curve C : x = 8 cos t, y = 16 sin t…

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Q: Find the derivative of this function

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Q: lim (3x + 1) sin(2x) 4x2

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Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e2x –…

A: Solve the exponential equation algebraically.

Q: 59-64 Use Property 8 of integrals to estimate the value of the integral. x'dx 60. | Jo x+4 59. dx…

A: ∫xn dx = xn+1n+1 +C ∫tan x dx =ln sec x+C

Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

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Q: Use the One-to-One Property to solve the equation for x. 3x - 1 = 27 %3D X =

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Q: 2x2 +4x - て +2

A: To evaluate the given integral.∫2x2+4x-3x2 dx

Q: (2xy+x^2+x^4)dx - (1+x^2)dy=0 the answer should be

A:

Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

Q: 3. 1- xZ dx

A: The integration of the integral is x4sqrt(1-x2), limit from 0 to 1.

Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

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Q: Consider the piecewise-defined function Jr+3, |1- x, x 0. (a) FUNCTION, so it must pass the…

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Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.

Q: A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it…

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Q: Let f (x, y) = e(8x-9y). Find the equation for the tangent plane to the graph of f at the point…

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Q: Consider the parametric equations below. Assume that t can be any real number. x=t-3, y=2t-5…

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Q: k(u) is a degree 3 polynomial with k(0)=-21.24 and zeros 4 and 3i. Find an equation for k with only…

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Q: If x + 1 f(x) then find the global maximum of on the interval [1, c0) Write DNE if there is no…

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Q: Apply the Ratio Test to each series to determine whether the series converges, or state that the…

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Q: The velocity of a car is v(t) = 42(t - 2)(t - 4) miles per hour on the time interval [0, 4] hours.…

A: We need to find distance traveled by car.

Q: E(-1)n+1_2 Vn n=1

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: Evaluate the limit: r(t + h) – r(t) lim h >0 for r(t) = (t°, sint, 1) h r'(t) = (

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

A:

Q: (2) Prove that for any integer L () NTX / sin? dx = L. L -L

A: ∫ cos(ax) dx = 1a sin(ax) +C

Q: Assume that f(x)dx = 3 and g(x)dx = -2, find the following: 1. Sf(x) + g(x)]dx = 2. S12f(x) – g(x)]…

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Q: -Ive the derivative dy for the function: x dx = e'sint ; y = ecost %3D

A: To find dy/dx.

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

A: Solution: ∯∂∂x6xy -∂∂y3xydxdy   (By green's theorem)

Q: ||r(t) × r"(t)|| ||r'(t)||* Use the formula k(t) : to find k(t). r(t) = e"i+ ej K(t) :

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Q: Evaluate the logarithm at the given value of x without using a calculator. Function Value f(x) =…

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Q: Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as…

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Q: |r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = ei + etj 30 е4 K(t) : e-t (25 el2t + 1)

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Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

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Q: 13. Find the length of the curve y4 + 8 from y = 1 to y = 4. X = 4y2

A: To find the length of given curve.

Q: 1) lim x100+500 ex

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: mparison test to determine whether the given series conve:

A: Please refer to the image below