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

Q: Find the average value of the function f) = 8-7 on the interval [0, 9]. %3D

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: A detailed solution is given below

Q: Evaluate: 3 A 1–x*) 2 + C 3 (1-x*) ² + C --(1-x*) ² +C D 1-x*) 2 + C 3

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Q: + 3x² 4)dx

A: Given query is to find the value of the integral.

Q: / (3V-1)dt is 3- 1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of 3…

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Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: Given : f(x)=7x+1   To Find : a) Derivative of f(x) b) Tangent at point (a,f(a)) where a=5

Q: Question 2 Determine the derivative of sec(x) tan(x) O sec z + sec z tan? x 2 sec? z tan x sec x O…

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Q: Solve the separable differential equation dy 0.7y, and find the particular solution satisfying the…

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Q: 4. , kr+2{cd= -3

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Q: Find V· (F x G), if F(x, y, z) = 6xi+j+15yk and G(x, y, z) = xi + yj – zk. V · (F × G) =

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Q: sin 201/1+ 2 sin 0/cos? 0 (sec² 0 – 1) d0 1. |

A: To find the following antiderivative.∫sin 2θ1+2 sin θcos2 θ sec2 θ-1 dθ

Q: dr 2 Vr*+3

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Q: Find the unit tangent vector to the curve at the specified value of the paramet r(t) = 4 cos(t)i + 4…

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Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: 2. A force of 5.0N is applied at the end of a lever that has a length of 2.0meters. If the force is…

A: We need to find the torque when we are given values of force  & length of liver and angle to the…

Q: 16z Consider the function f(x) = x°e f(x) has two inflection points at x =C and x = D with C<D where…

A: 1) The given function is:…

Q: xe - ye" = In(xy). Find dy/dx.

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Evaluate the line integral -ydx + xdy along the curve C: y? = 30x from (30, 30) to (0,0). NOTE:…

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Q: A spring with a natural length of 10 cm, is stretched by ½ cm by a 12 N force. Find the work done in…

A: Given query is to find the work done .

Q: dx 2. (x-1)% (x- 1)

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Q: Given the function + y-4, find y'. Oy = Oy =

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Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x – y)dy for the given path. C: x =…

A: Let's find.

Q: Evaluate the integral (12x + 6y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Find the equation which satisfies the separable differential equation dy – 18x dx with the initial…

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Q: Describe the graph of the equation. r = 9 sin 13t i - 9 cos 13t j

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Q: Compute (a) a1 and (b) r2 for the iterative process defined by an +1 = 2an(5 – an) with æo 3. 10z, –…

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Q: Find the 73rd derivative of the function f(x) = 2 sin(x). f (73) (x)

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Q: x³dx Using trigonometric substitution, is equivalent to x²-4 8 / sec*o do A B 6 tan'o seco do © •Smo…

A: The given integral is: I=∫x3dxx2-4

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: Solve

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Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

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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: Question 3 Determine the derivative of In(csc x) cot x Csc I - cot x CS z Previous

A: A detailed solution is given below

Q: Answer the following questions for the function f(x) = a/a? defined on the interval -4 < x < 5. x+16…

A: We need to find concavity and inflection points.

Q: domain: vertical asymptotes l:  x= horizontal asymptotes: y=

A: Given query is to find vertical asymptots and horizontal asymptote.

Q: af(x, y) If f(x, y, z) = , then is equal to dz

A: Given,  f(x,y,z)=x-zy-z

Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

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Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: For the given function find dy/dx. = x +2

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Q: Describe the graph of the equation. r - 12cosri + 5sinsj -k O tis an ellipse in the z = -1 plane,…

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Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

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Q: Represent the following equations in R? by a vector-valued functions. Imet gaoglecomis shwing your n…

A: Given

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: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. f(x) = cot x, a = - Po(x)…

A: As we know that; The Taylor series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at x=a.…

Q: Find a value for k that will make the given function a probability density function. f(x) = kz, on -…

A:

Q: [x+1

A: The objective of the question is evaluate the indefinite integral.     Note -  As per our guidelines…

Q: Find the derivative. 8 + ex y = In 8 - ex Step 1 The given function y = In 8 + ex can be written as…

A:

Q: Describe the graph of the equation. r = 12 sin 6t i – 12 cos 6t j O Itis a circle of radius 6 in the…

A: To find: Discribe the graph of the equation