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)

Q: dx 5-x?

A: We will solve the integral.

Q: V11 T Use the information given about the angle 0, sin 0 = 4. <0<n, to find the exact values of the…

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Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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Q: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

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Q: (1) fx sin x dx

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Q: 2- Sinx-y cos?x =.

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Q: tan 0 d 30. dO sec² y dy

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Q: 5. Í sin 2e de 6. ſer cosh x dx

A: We have to integrate and have to check the answer

Q: Please

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Q: Which identity is most useful in evaluating sin² x dx? sin? x + cos? x = 1 cos 2x x = 1- 2sin? O…

A: The given integral,         ∫sin2x dx

Q: Let y=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

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Q: 13 1 dx 13 – x

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Q: For f and g defined below: 15V 10 y = g(x) -10 10 15 y = f(x) -10- g(-5) is undefined. f(15) is…

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Q: Find the value of the following definite integrals. Show your solution. 1. L* + 4) dx 2. f(cos x +…

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Q: x² Consider the function f(x) = x² –1 (a) Find the intercepts of the graph of f (if any). (b) Find…

A: This is a problem related to function calculation. Based on the general formula and concept we will…

Q: ニ。

A: Given query is to find the solution of the differential equation.

Q: dy ーy+x? -yx? ーソX

A: Given: dydx=1-y+x2-yx2

Q: Q2) Find the integral of: f*,6 tan*x dx

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Q: Evaluate the definite integral. 12t dt O el2 – 1 (e-) - 1) + 2 – 1 i - (e" - 1) j +k 12 O el2 12 O…

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Q: dg 1+sin 2x Find of g(x) dx 2x-tan 2x

A: To find the derivative of given function.

Q: completely

A: We will solve the integration.

Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

Q: 2. Find the r educed echelon form of the fo A = 0 0 0 6 54 0 (714161 Show your working

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Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

A: Write the nth term and  add them to get Sn .

Q: Q2: Solve the following integrals:- (2) fd 4x2-9 xp: (3)fx sin(x +1)dx

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Q: d. [r:(t) r2(t)] and r:(t) x r2(t)] first by differentiating d Calculate dt the product directly and…

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Q: 1 Find the Fourier series for 1, if -п <х <0 { { -1, f (x) = -1, if 0 < x< n

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Q: (-5 S + (0.9)" | lim

A: Given query is to find the value of the indicated expression.

Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x² – 9…

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Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: Problem 5 Part 1: Consider a cost function where C(x) in Philippine peso is the total cost of an…

A: Let's find.

Q: Q2: Solve the following integrals:- (1) fx² sin x dx (2) f dx 4x2- xp: (3)f x sin(x + 1)dx

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Q: Evaluate sin? xcos xdx .

A: To evaluate: ∫sin2x cos3x dx=∫sin2x cos2x cos x dx=∫sin2x (1-sin2x) cos x dx

Q: Solve tan(x)=5in the interval osxs360°,giving your solutions to 2 decimal places

A: Given,  tanx=5 x=tan-15 x=78.69°

Q: x-1 dx (x+1)5(x-3)5

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Q: 1. Let -7 3 -3 2 C = 4 A = B = -3 -3 Determine which (if any) of the following matrices are well…

A: The solution is given in the nwxt step.

Q: Condense the expression to the logarithm of a single quantity. log (x + 1) + 2 log3(x - 1)] + 6 log3…

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Q: Find all the relative extrema and saddle points, if any, of the given function below: f(x, y) = In(x…

A: To find all the relative extrema and saddle points, if any, of the given function below:fx,…

Q: Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find dw/s and dw/at by using…

A: Using chain rule and converting function in term of s and t are differentiated.

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: a b c Given det d e f = 5, find the following determinants. h i a b det d. e f -3g -3h -3i a b det…

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Q: Find div F and curl F if F(x, y, z) = 17y*z4i – 3x°z®j – 3xy°k. - div F= curl F=

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Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

A: To differentiate.

Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: The graph of the function f (2) = 2 arcsin(x – 4) +1, is best pictured by:

A: We will put the x values and get the f(x) values.

Q: dzy What is dx2 for the curve given by x = t2 and y = t3?

A: Our Aim is to find d2ydx2 for the curve given by x=t2 and y=t3

Q: Use the One-to-One Property to solve the equation for x. (Enter your answers as a comma-separated…

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Q: e- + cos (xy) = (4 – 3z) (2 + 2.x), UIM 4. find ду ÚTM az cos (ху) — (4 — 32) (2- 8 UTM UT UTM

A: Partially Differentiate with respect to y

Q: 2. S(e" + e-3)² dt

A:

Q: xdx 41. 12-х

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