Question 1 lim xe-* X→∞ A. 0 = B. Co C. e-1 D. e E. 1 F. None of these.

Q: •oodwi For any real sequence, lim Xn Yn = Tim (x₂) tim(yn)

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Q: Find an integrating factor and solve the equation 4x y' = e¹x + 8y - 1.

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

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Q: Write the first three terms of the sequence. an = 5n-4 2 n² +4 a3 The first three terms are a₁ = ₁a₂…

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Q: Determine whether the series DIVERGES.) 00 n=1 חל - 6 14" = n=1 6-77 147 129 Tutorial converges or…

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Q: 6. Find the limit (if it exists) of the sequence (x_n) where x_n = (2+3n-4n^2)/(1-2n+3n^2).

A: We have to find the limit of the sequence.

Q: For the given functions f(x) = − 9x², g(x) (1) (fog)(x) = (2) (gof)(x) = (3) (ƒ ○ ƒ)(x) = (4)…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: Consider the following. y = x² y = 12 - x K 16 14 12 -2 10 B 6 4 2 2 8 10 12 (a) Find the area of…

A: To find the area of given region.

Q: Question 3 of 10 ♫ lim f(x)=-1 -2 Given find the following limit 3/7f(x)-g(r)² g(x)+1 and lim g(x)=1…

A: The given data is: limx→2fx=-1limx→2gx=1  Use the property of the limits to find the value of the…

Q: x= 4+² +7, y=t, t = -1 Write the equation of the tangent line. What is the value of dx² d²y dx² at…

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Q: Find the absolute minimum of the function f(x)= = 02 GW/N 0.3 4 O 1 0-2 01 2 2x x2 +4 on the…

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Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: 80 1 n+8 Does the series (-1) converge absolutely, converge conditionally, or diverge? n=1 Choose…

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Q: Find ду ах if 2 Y = (x²+1) • 1₁ (x² + 1) In

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Q: Given f(x) below, find f'(x). Provide your answer below: f'(x) = = sin(x) f(x) = to dt

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Determine the limit of the sequence or show that the sequence diverges. If it converges, find its…

A: we have to check sequence is convergent or divergent.

Q: Are the partial derivatives and gradients of a function the same, no matter your starting position?

A: Topic:- application of derivatives

Q: 6. If u = given by x = +2, where x+y+z= 1, prove that the stationary value of u is y b a+b+c' a…

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Q: At value of a does the curve y = 2√4x2+1 have a tangent line with a slope of 2? O √12 00 O /12 O…

A: To find the slop at given point.

Q: Jamie and Marlene are having an ice skating contest. They skate along a long, straight track and…

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Q: Evaluate the integral. (Assume a b. Remember to use absolute values where appropriate. Use for the…

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Q: f(x, y) = -(x - 7)² In² (y + 4)−(4x + 7y)². a) Find all the first partial derivatives of the…

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Q: Solve given differential equation. ydx-xdy+2dx=0 

A: The objective of the question is solve the differential equation.

Q: Analyze the continuity of this function. If there are discontinuities, state the type. x² + 2x x≤1…

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Q: Alexandra invested $1,100 at the end of every month into an investment fund that was earning…

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Q: Let f(x) = x + 1 x + 6 f-¹(-10) =

A: Let's evaluate the inverse of function  value.

Q: Apation car is parked 65 feet from a long warehouse (see figure). The revolving light on top of the…

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Q: h(x, y) = x²7xy - y² relative minimum relative maximum saddle point (x, y, z) = (x, y, z) = (x, y,…

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Q: x = 6 sin is an appropriate trigonometric substitution for the integral Select one: True O False 1…

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Q: Evaluate the integral. (Assume a b. Remember to use absolute values where appropriate. Use C for the…

A: Given ∫4(x+a)(x+b)dxTo evaluate the integral:

Q: Find the E.I. of the following periodic signal -2 -1 1 2

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Q: Calculate the first three partial sums of the series. S₁ S N' 11 = S3 = Σ n = 1 n+4 Use the sequence…

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Q: 1 √1/₂ y+4 y² + y dy felt +2e²t

A: The given integral is a (y+4)/(y2+y).

Q: Find d dx d dx 0.8 0.8 √x -3.4x -3.4x2+6x + 6x

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (3.-1.1)…

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Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

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Q: Question 8 of 10 Calculate the appropriate limit to determine the equations of any horizontal and e…

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Q: Let R be the region bounded by y = 4 – x², the x axis and the y axis. 3 2 1 = The solid obtained by…

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Q: Find lim lim h-0 h→0 f(6+h)-f(6) h f(6+h)-f(6) h if f(x)=x² +4. (Simplify your answer.)

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: This is a problem related to linear approximation of the function. Based on the general formula and…

Q: Find a formula for the nth term of the sequence. 1,-4, 9, -16, 25, ... Determine the sequence's…

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Q: Use the Root Test to determine if the following series converges absolutely or diverges. n² 00 n=1…

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Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Select the correct answer. dg(x) dx dg(x) dx dg(x) dx = casi(v) 4 = 4x sin(x) 5 = x sin(x) g(x) = ft…

A: using fundamental thereom of calculs,

Q: Find the solution of the given initial value problem 50y" + 15y"+y' = 0, y(0) = -2, y'(0) = -10,…

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Q: 7. The value of f √x dx 1+√x A. x-2√x + 2 ln (1 + √√x) + C B. x-2√x -2 1n (1 + √√x) + C C. x-2√x+2…

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Q: Find y ay ax Y = (x²+1) • In (x² + 1) if

A: We know that derivatives power rule is  d(xn)/dx = nxn-1. And also know that: d(lnx)/dx = 1/x.…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: To find the value of dy/dt in first case and value of dx/dt in second case.