Find the derivative of: 3 sin (– 3x). Hint: sin (x) = [sin(x)]"...so use the chain rule (twice!).

Q: 5) Find tue soletion of the differen tiel equation dr Sec't which paffes dt fant +1 turough the…

A: Solve the differential equation by separation of variables.

Q: Determine the convergence or divergence of the series. (If you need to use co or -0o, enter INFINITY…

A: limn→∞ sech(n)=limn→∞ 2en+e-n=limn→∞ 2e∞+e-∞=limn→∞ 2∞+0=0limn→∞ sech(n)=0

Q: Evaluate the definite integral. Use a graphing utility to verify your result. U-5 np

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Q: 1 dx X +x13

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Q: Use the limit comparison test to determine if the series converges or diverges. 00 22) E 6n3/2 + 7n…

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Q: V3x - 2 lim tan- %3D x + V3

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Q: (2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

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Q: y = x and y =x+2 ve the area about the line x = 3. Using cylindrical shell method, the volume of the…

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

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Q: dy -1

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Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: Find the limit. If the limit does not exist, type DNE. lim (1,9) →(-4, -2) 32 – 5zy =

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Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

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Q: Find V. (V x F) if F(x, y, z) = 8 sin zi + 6 cos(2.x – 3y)j + 7zk. V.(V x F) =

A: Vector

Q: Problem 3. A stone is dropped in a lake, creating a circular ripple that travels outward at a speed…

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Q: 4) Find all values in the interval [-27,27]at which the graph of f has a horizontal tangent line.…

A: topic- functions and derivatives

Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

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Q: 71 dt Find F (x) and F (-2). 14. Consider F(x) .Co 1+t5 EGO

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Q: Determine the convergence or divergence of the series. (If you need to use o or -co, enter INFINITY…

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Q: Use the definition of Taylor series to find the first three nonzero terms of the Taylor series…

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Q: Determine the convergence or divergence of the series. (If you need to use

A: answer is in next step

Q: Question 2 x2 Consider the function f(x) = x² –1 " (a) Find the intercepts of the graph of f (if…

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Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: Consider the function f(x) = cos(3 x). (a) Give the derivative of this function. f'(x) = | (b) Find…

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Q: Find the second and third derivative of the function (a) f(x) = x6 – 3.x5 – 41x – 73 - |

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

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Q: Find f'(2).

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Q: Find div F and curl F if F(x, y, z) = xz°i + 2y°r*j+ 6z*yk. div F=2° + 16 y' x+ 12 zy curl F=

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Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: 8) Fiad the volume of the solid gonereted by revelving the regien beunded by tue graphs of equetians…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the graphs…

Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: 1 Σ 6" - 5 n = 1 8

A: Given :

Q: Consider the lines l : = 2 – y = z +1 and l2 : y - 2 3 1. Determine a direction vectors for the…

A: Consider the lines L1: x-12=2-y=z+1 and L2: 1-x2=y-2=z-33.1 To determine a direction vectors for the…

Q: Show that the function f defined by (x, y) = (1, – 1) f(x, y) = 1² + y (x, y) # (1, –1) I + Y is not…

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Q: Express the series using sigma notation. 5 + 8 + 11 + 14 + 17 25(3) n-1 5 23n+2 n-1 23n+2 n-1 C5(3)1…

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Q: Find div F and curl F if F(r,y, z) = 1°i – 7j + yzk. div F= curl F=

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Q: Evaluate the limit V5 + 7x² lim 5 + 4x I+ 00

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Q: alculate the Laplace transform of each of the followir a. 7t b. e' sin(t) c. u(t - 3)e2

A: We can  solve 2 problems only.

Q: from e'dv Ve4v -16

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Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

Q: 18. Find xV4x -3 dx 18. SxV4x - 3 dx

A: Use substitution to solve

Q: Evaluate the following limits. If needed, enter oo for oo and -oo for – 0. V5 + 6x2 (a) lim 3+ 10x…

A: Use the substitution and then simplify the limit.

Q: sec 1.)S Intanßtanß dß

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Q: State where the power series is centered. (-1)"(2n – 1) „n Σ * 2"n! n = 1

A: Solving

Q: 1 If x= tand , then dr coso do . (1+x²) ½° A True B False

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Q: S V9x² + 64

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Q: p.564/ use Trapezoidal method and Simpsons' rule to evaluate.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Determine the vactor feld of F. F(z, y) = yi - j

A: This is a problem related to vector field calculation. Based on the general concept we will provide…