Find and prove the limit or deteremine if the limit doesn't exist: n/(e2n-5)

Q: Given that f(x) = x³h(x) h(-1) = 4 h'(-1) = 7 Calculate f'(-1).

A: given data f(x) = x8h(x) h(-1) = 4 h'(-1) = 7 find f'(-1) = ? here we have to find the derivative of…

Q: The DE 7x (-7in(2y) - 4e) dx = (2x +2y dy y is an exact differential equation. Select one: True

A: Given ( -7ln(2y) - 4ex )dx = ( 7x + 2yy)dy( -7ln(2y) - 4ex )dx - ( 7x + 2yy)dy = 0 standard form Mdx…

Q: Calculate the test-statistic, t with the following information. n₁ = 45, x1 = 2.52, s₁ = 0.57 n2 =…

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Q: (2) Suppose you lift a laptop that weighs 3.7 pounds off the floor onto a shelf that is 2 feet high.…

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

Q: Make a sign diagram for the derivative of the function f(x) = x3 - 3x2 -24x+7 including all open…

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Q: Let f(x) = (sin x)³ + (cos x)³ Enter the total number of critical numbers on the interval [0, 2π].

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Q: Question 1 equation : y cost + 2te" + (sint + t²e" - 1)y' = 0. S. Consider the differential a) Show…

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Q: Find the points of local and/or absolute maximum and minimum for the function_ƒ(x) = x² + over…

A: See this solution in below.

Q: Find the points of local and absolute maximum and minimum for the function f(x) = x² + ²/ over…

A: The given function is:f(x)=x2+2x ;            over  1, 4

Q: f(x) = 36x + 3x2 - 2x3 a) Find the intervals of increase or decrease b) Find the local maximim and…

A: see below the answer and calculation As per Bertleby Guideline I have to solve first three subparts.…

Q: Calculate / cot cot³(x) csc³(x) dx. Your answer should be in terms of x.

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Q: Use the First Derivative Test to find the location of al local extrema for the function given below.…

A: Topic = Functions

Q: Use spherical coordinates. € /// * Evaluate xyz dv, where E lies between the spheres p = 4 and p = 8…

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Q: Use the graph of the function f shown in the figure to the right to estimate the indicated function…

A: Given graph:-

Q: Find the values of x for which the series converges. (If the answer is an interval, enter your…

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Q: Find the points of local and/or absolute maximum and minimum for the function f(x)=√9-x over [1,9].…

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Q: -3x+1 Given y=6³+¹, find y".

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Q: lim In(x) In XX x+1 + 1 X --

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Q: Use logarithms and a calculator to solve for the value of x. If an answer is not exact, round your…

A: Since you have posted multiple questions, we are supposed to only first three questions. If you want…

Q: 11. Consider the region bounded by f(x)=x² and the x-axis over the interval [0, 2]. Suppose the area…

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Q: 1. Let f(x)=√(x - 1)² with domain [a, b], where a = -1 and b = 3. (a) Is f(x) continuous on its…

A: The given function fx=x-125 with the domain -1, 3. We have to find the required values using Rolle's…

Q: Q1: Find the divergence of the function G(x, y, z)= P(y, z)i + Q(x,z)j + R(x, y)k where i, j and k…

A: Solution : Given function is

Q: The graph of f(x) = -4(0.45) is given below (click on graph to enlarge): Let g(x) be the reflection…

A: Given the graph of fx = -40.45x is

Q: Bernoulli's equation dy dx -ye-2x = 6y8, will be reduced to a linear equation by using the…

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Q: The radius of a spherical balloon is decreasing at a rate of - in/sec. π Which of the following is…

A: given  negative sign because radius is decreasing

Q: Find the absolute extremum, if any, for the following function. f(x) = 4x - 7 Select the correct…

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Q: dG dx If g=- which of the following is equal to d dx -tanG?

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Q: Let 72 f(x) = 9xe6 Find all critical numbers and inflection points of f (x). Enter the largest x…

A: The given function is: fx=9xe-x26

Q: Use differentials and the graph of g' to approximate the following, given that g(3) = 4. (Round…

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Q: 32. The vectors (6, 4) and perpendicular. Find k.

A: Given that the vectors are perpendicular

Q: for each In Problems 21-30, find an explicit formula a, = sequence, determine whether the sequence…

A: The given sequence -1, 23, -35, 47, -59,..... We have to find the explicit formula for the sequence…

Q: Find the work done for a force F = 12 x2 N from x=2 to x =6 m.

A: Given query is to find the work done .

Q: 3. Sketch the graph of a continuous function f(x) with domain [0, 2] which is differentiable up to…

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Q: Sketch a graph of a function f(x) such that f'(x) > 0 on (-4,-2) and f'(x) < 0 on ( - 2, 3) Note:…

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Q: Determine all the critical numbers of f(x) A) X=1 B) X=0 (C) x=-1 D) There is none 1+x² Select all…

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Q: Question 1 equation : y cost + 2te³+ (sint + t²e - 1)y' = 0. Consider the differential a) Show that…

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Q: Question 2 differential equation 2 = y² + ¾/7 y y² + y = 1: Consider the following a) Is the given…

A: The given differential equation is:1ty'+2t2y=t4e-4ty-3

Q: 2. y"+3y"+4y+2y=0; y(0) = 4; y'(0)=-4; y"(0)=1 a. y=e** (4+sin x) b. y = 4e* cos x c. y=e*(1+3 cos…

A: We need to solve D.E.

Q: The standard form of the linear DE dy 4- dx is Select one: O True O False dy dx = 12cos(x) - 16x²y +…

A: To find standard form of linear D.E.

Q: Let a and 3 be first quadrant angles with cos(a) Find cos(a - B). Enter exact answer, or round to 4…

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Q: Find the differential of the function f(x, y) = yeª at (0, 3). df =

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Q: For the function dx The answer cannot be found among the other choices. y4/3(2x (xy) 2/3-x 4/3y) x…

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Q: Find and classify the critical points of the function f(z,y) = y^-32y

A: Solution: f(x,y) = y4-32y+x3-x2 Critical points are points where the function is defined and its…

Q: Determine whether the series converges or diverges: Input C for convergence and D for divergence: 00…

A: The given series ∑n=1∞-1n2n9n+3.

Q: tons interval −4 < x < 2. For parts (b)-(e) use the graphs in part (a) and include a brief(!)…

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Q: Use integration by parts to evaluate the following integral. 1 18 U= 0 x In 18x dx Determine u. ...

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Q: Suppose f(x) is continuous on [-1,3] such that ƒ ( − 1) = 4 and ƒ (3) = 7. By the IVT, we can…

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Q: Find the critical points in the domain of the function: y=4-x³-3 -3.x. If there are no critical…

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Q: check

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Q: Determine all the critical numbers of f(x) = A) X=0 B) x = 1 (c) There is none (D) x=-1 3x x²-1 .…

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