S Find sec42x -dx tanº2x cot²2x-cot82t+C 12 16 1 1 1 1 12 tan 62x 16 tan 82x --(cot$2x) (² 1+3csc²2x 12 4 cot82x (4sec 22x-1) -(cort2x 4 12 + + C +C +0 +C

Q: 3) f(x, y, z)=x² + y² -2=²+ = ln(x). (1,1,1) -1/2 4) ƒ(x, y, z)=(x² + y² + =²)¯¹¹² +ln(xyz),…

A: 3)    fx,y,z=x2+y2-2z2+zlnx We have,       grad∅=∇f=i∂f∂x+j∂f∂y+k∂f∂z ∂f∂x=2x+zx ∂f∂y=2y…

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A: We have to find k(t)

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A: Topic:- algebra

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A: I am attaching image so that you understand each and every step.

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A: We are aske dto find the curvature and radius of the curve.

Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: Let ƒ(x) = 4x² + 3x³ +9. Find the equation of the line tangent to the graph of y = f(x) at the point…

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Q: 22-12x To solve S; x²(3x²-10x-8) form of the partial fractions for this integral? A(2x) + B C D (A)…

A: ∫22-12xx23x2-10x-8dx

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A: Solution is here

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A: Theta lies  in second quadrant ot in four quadrant . First find the trig ratio considering the theta…

Q: 1 2x²-3 √² ²3 dx = (x² + 3)² + ²x² ³ + d x+√√x²+3 27 x²

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Q: Find all six solutions between 0 and 2 for the trigonometric equation: sin(30) = Use the multiple…

A: The given equation,      sin3θ=12

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A: Given that,

Q: Question 16 A line through (-1, -2) with a slope of -10 has a y-intercept at

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Q: +3x²+7x+28 18. Using partial fraction in evaluating x³+x²+7x 1/2(2x + 1) - 17/7/2 6-2x -…

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Q: The ghien matrix is an augmented mutris representing a system of linea equations. Write the matrie…

A: To find the reduced row echelon form of the given augmented matrix .

Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: S sin (Inx) dx? How many times will you perform integration by parts to evaluate

A:

Q: How many times will you perform integration by parts to evaluate sin (Inx) dx? A 4 (B 2 1 3

A:

Q: Use the root test to determine whether the series 2n 4n + 9 converges or diverges. 9n + 2 n=1 Since…

A: Root test : Suppose that we have series ∑ an .Define,                 L = limn→∞ ann = limn→∞ an1n.…

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A: The given function,    fx=3x2-1

Q: 15x²x³43x - 19 can be rewritten as (x + 1)²(x² - 6x +13) Ax + B C D Slax ² + + lax² + bx+c (mx + n)t…

A:

Q: g(x) a b Suppose g(x) = f(x) +3 a= 2 and b=7 Compute the area between fand g using 2 and 7 as your…

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Q: If t is in years, and t = 0 is January 1, 2005, worldwide energy consumption, r, in quadrillion…

A: We need to solve integral porblem.

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A: Given

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A: The given series,        ∑n=1∞-7nnnxn

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A: Solution of given question is written in below steps.

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A: Let's find.

Q: Sketch a graph of f(x)=(x-2)² +4 6.

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Q: 25 √x²√5 − x²dx = − x(5 - x²)(5 − 2x²)+² Arcsin(x)+c

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Q: Use the ratio test to determine whether n3n (n + 2)! n=29 converges or diverges. (a) Find the ratio…

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Q: Explain why you think the series Σ01 77 converges to a finite number (-8)"-1 or diverges. If the…

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Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

A:

Q: S 1 xvx²-2x dx = √x²-2x X +C

A: To prove that ∫1xx2-2xdx=x2-2xx+C

Q: Evaluate the definite integral. NOTE: Enter the exact answer. | ti + t²³j|| dt = [

A:

Q: c. The region R enclosed by the curves y = x and y = x² is rotated about the line y = 2. Find the…

A: Using disc method, volume of solid is evaluated.

Q: Using integration by parts, Then k is? (a)-1.5136 [²x³ cos(x²) dx = k - [*²x sin(x²) dx (b)-1.1365…

A: Our Aim is to find the value of k by evaluating the integral using integrationby parts.∫02 x3 cos…

Q: 1. Evaluate the following limits. Using L'Hôpital's Rule is not allowed 3. lim (x-3) tan(9-x²)…

A: We will calculate the limits by Limits rule

Q: r₁(t) = cos(t)i + sin(t)j +5tk, r₂(t) = 4i + tk X d -=[r₁(t) · r₂(t)] 10 t - 9 sin(t) = dt d -[r₁(t)…

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Q: Find the average rate of change of g(z) = 4x + 5 between the points (-4,-11) and (3,17)

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Q: √a²-x² -dx √a²-x² X --Arcsin (). + c

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Q: Consider the following system of linear equations 4 4 -2 30 1 0 18-0 7 -2 -3 2 -18 Which one, among…

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