Test the given geometric series for convergence or divergence. If it converges, find its sum. 4 16 64 +... +.. 81 729

Q: tan () (9) sin (4) F. Evaluate the integral r2 cos ()

A: integration

Q: 10 Find the derivative f' (0) of f(x) = at х+4 O using the laws of differentiation.

A: f(x)=10x+4DIfferentiate w.r.t.xf'(x)=ddx(10x+4)Take constant outf'(x)=10ddx(1x+4)f'(x)=10ddx(x+4)-1…

Q: 1. f(x) = V3x +2 2. f(x) = 2х-3. 4 %3D 5x+1

A: We know quotient rule of differentiation as follows  ddx{f(x)g(x)} = g(x) f'(x) - f(x) g'(x){ g(x)}2…

Q: Use the method of Lagrange multipliers to maximize the function f(x,y,z)=4x+2y+z subject to the…

A: Let's find.

Q: 3 c2x S *x² dy dx 4.

A: Integral

Q: Use differentials to find the approximate value of y: (2x – 1)* when x = 0.98. O (E) None of the…

A: Given :f(x)=2x-14x=0.98

Q: dx 8. Evaluate the integral / zlnrV(In x)² – 8 x In a V(In a)2 – 8 |

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Q: y =, x = 1, x = 4, and y = 0 is revolved about the y - axis.

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Q: LEARNING TASK 1: Determine the antiderivatives of the following functions: 1. f(x) = (x+1) 100

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (- 3, 4, 3), Q = (6, 6,…

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Q: Step 2: Step 3: Sten 4:

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Q: Find an implicit and an explicit solution of the given initial-value problem. dy y – 1 dx x? - 1'…

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Q: (c) Let f(x) = In(x + 8). (i) Find the domain and range of the function. (ii) Find the inverse of…

A: Let's find.

Q: x3-1 dx J2+2x+5

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Q: A supermarket sells two brands of granola: brand A at $p per pound and brand B at $q per pound. The…

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Q: Consider the function f(x) = The value of f'(0) is: (x+ 1)2

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Q: dA

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Q: Find, the genetal Solution o the differehtial equation (2x+Y-3) dy= +2Y-3)dXf %3D

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Q: 2. For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). x = 3t? –…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: S 23x26 + 35 + x2-16 dx x-4

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Q: y=v16-x 2.

A: This question is based on application of integration.

Q: A. For each of the following functions z, find and дх 2. z = tan 出一郎

A: Explanation of the answer is as follows

Q: Compute the area enclosed by the curves. You must show your work. Express your answer as a fraction.…

A: In this question we have to find the area enclosed by the curves.

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know that; The expression for the volume of the cube is: V=a3    ....(1) Where a is the edge…

Q: A particle is moving with acceleration given by the function a(t) = sin t - 3t. Find the position…

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Q: #2

A: To find out the integration.

Q: 3. f(x) = (2x + 1)3 4. f(x) = V7 + V3x + 1

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Q: Find the volume OF the solid obtained by rotating about the y- axis the region bounded by Y= x2 and…

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Q: sin 2t sin 5t 20 s4 + 58s² + 441 None of the choices Option 3 10 1 s4 – 58s² + 441 2 s2 + 32 s2 + 7?…

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Q: 2. y=x² - 4x and y=-x² +2x. y² = x and x² –2x+3y= 2. 3.

A: Given÷

Q: Find the length of the curve 7(t) = (2 cos(4t), 2 sin(4t), t) for –2 <t s8 Give your answer to two…

A: As we know that; The expression for the length of the vector-valued curve; L=∫abx't2+y't2+z't2dt And…

Q: y = e* – axis. and the x - axis is revolved about the y

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Q: PART

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Q: Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE.) 10x3…

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Q: Determine dydx of function g 1 g(x, y) = cos (Tx ) + log3 (x – y)

A: We will use simple differentiation rules to solve this question.

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: 3 Use the linear approximation to estimate Af = f(3.1) – f(3) for f(x) = I+x (Use decimal notation.…

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Q: Solve the given initial-value problem y' + (tan.x)y = cos²x, y(0) = -1

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Q: (t- 1)* 24 24 4 24 24 4 1 85 84 g5 84 82 O Option 1 O Option 2 24 24s 12s² + 4s3 + s4 12s2 + 4s3 + s…

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Q: dz az and ду Suppose z is a function of x and y, and tan Vy? + x2 = ze6y. Solve for

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Q: az and ду az A. For each of the following functions z, find ax 1. z= sin3x cos4y 2. z = tan- (2) 3.…

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Q: The following question is about the rational function (x + 1)(x - 2) rex) = (x + 2)(x – 6) The…

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Q: Use the Linear Approximation to estimate Af for f(x) = , when a = 2 and Ax = 5+x2 (Use decimal…

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Q: Use a calculator to find the approximate value of the expression. Round the answer to two decimal…

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Q: 4. Determine the equation of the plane passing through the point (1, -4, 3) and parallel to the…

A: To determine the equation of the plane passing through the point 1, -4, 3 and parallel to the plane…

Q: Find the Laplace Transform of the functions PLS ANSWER ASAP

A: We need to find laplace transform.

Q: Find the nth term of the given infinite series for which n= 1, 2, 3, ... 1 1 +... 2x6 3x7 4x8 5x9 an…

A: Given 12×6-13×7+14×8-15×9+.....n is from 1,2,......... to infinity

Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

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Q: Find aly if and of to

A: Differentiation

Q: .4 dx 2 Vx2-2

A: Given:        ∫24dxx2-2 Apply trigonometric substitution:    substitute x=2sec u and dx=2 sec u tan…