6. a) Determine whether each series is convergent or divergent. Carefully explain your reasoning. n=1 1+3″ 1+4.3" b) ∞ Σ n=0 n-1 15√√n²³ +1

Q: Use the Comparison Test to determine whether the series converges. Σ K = 1 1 5k5+6 The Comparison…

A: The given series is ∑k=1∞15k5+6

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A: Find the limit from the graph

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Q: £f*. S: z = 18, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

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Q: Evaluate f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of t S g(s) = = = √³ (t -…

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Q: Plot four points and an asymptote. Then click on the graph icon. -9 8 1-6 LA 15 19 I 84 I 1 1 KL 71…

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Q: Find the directional derivative of the function at P in the direction of v. √2 2 f(x, y) = x³ - y³,…

A: Given problem:- Find the directional derivative of fx,y=x3-y3 at point P8,3 in the direction of…

Q: 7. Find the absolute maximum and absolute minimum values of f(x)=2x-322/3 on the interval (-1,2]).

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Q: Find the limit . Xy lim (x,y) →(4,3)x² + y² 12 125 ○ 25 이 12 b 5

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A: We need to find area.

Q: 18 0-17 ¹8 cos(x¹8+18) Question 6 Find the total differential for the function w = Odw - 262³ y sin…

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Q: up the iterated integrals for both orders of integration.  Then evaluate the double integral. D is…

A: Topic:- application of integration

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Q: Find the 11th term of the following geometric sequence. 2,8, 32, 128, ...

A: This question can be solved using the formula of general term of geometric sequence.

Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da

A: The given equation is x4+2y5x3=5y2

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Q: Given the g(x) function, what is the best estimate for the instantaneous rate of change at x=3? g(x)…

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Q: question 8 please

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Q: When you A B D E T R|N 2 None of the given choices Pa evaluate: 4 S²S²x² 0 0 xsin ²(y) dy dx the…

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Q: 2).  Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic equation for C =…

A: Given problem:- Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic…

Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the…

A: The general equation of function of temperature is given by÷ D=asin[bt-c]+d Now we need all the…

Q: 1- Find the inverse of Laplace transform of log s²+1 (s-1)²,

A: To find inverse Laplace transform:

Q: 3) .  A population of deer inside a park has a carrying capacity of 200 and a growth rate of 4%. If…

A: To find the population of deer at any given time, P(t).

Q: At which of the marked values of x is A. f(x) greatest? x = B. f(x) least? x = c. f'(x) greatest? x…

A: Note:- According to company guideline we can do maximum 3 sub parts so i am solving here first 3

Q: Problem 7. Answer: Find #L if y = 7x45

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Q: 400 - e 1 2x dx= dx, x < In 20 2x 400-e (Type an exact answer.)

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Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: A region bounded by f(y) = 2y – 2, y = 3, and x = 0 is shown below. Find the volume of the solid…

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Q: If  f(x) = 3x + 4 and g(x) = 5 x,  find f(g(x)) and g(f(x)). f(g(x)) =        g(f(x)) =

A: We have given  f(x)= 3x+4 and g(x)=5x  We have to find  1) f(g(x))  2) g(f(x))

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Q: For the function, locate any absolute extreme points over the given interval. (Round your answers to…

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Q: For the following equations, enter y if the equation defines y as a function of a but not vice…

A: To find : whether the given equation represents a function or not ?

Q: Consider the marginal cost function C'(x) = 400+ 12x -0.01x². a. Find the additional cost incurred…

A: Given  C'x=400+12x-0.01x2

Q: of a sequence and its series. Giver (An) is convergent. } is convergent.

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Q: When you evaluate: A B D B C None of the given choices E RIN 2 SST xsin ²(y) dy dx the results is 0…

A: The given double  integral is xSin2y, y from 0 to pi, x from 0 to 2.

Q: Rewrite the following as a sum of trigonometric functions with no powers greater than 1. cos² (2x) =…

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Q: The following equation is given. Complete parts (a)-(c). x³-5x²-9x+45=0 a. List all rational roots…

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Q: Find all numbers c that satisfy the conclusion of the mean value theorem. f(x) = 2x2 - 5x + 1, [0,2

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Q: Problem E4 Proof that: cos³x+sin³ x cosx+sinx + cos³ x-sin³ x cosx – sinx = 2

A: Given  cos3x+sin3xcosx+sinx+cos3x-sin3xcosx-sinx=2

Q: Find the maximum and minimum values of the function g(0) = 30 – 7 sin(0) on the interval ㅠ [0, 1]. 2…

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

Q: Use the Ratio Test or the Root Test to determine whether the following series converges absolutely…

A: Let's find series is converges or diverges.

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis…

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Q: Let R be the region bounded by the following curves. Use the method of your choice to find the…

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