Evaluate the limit. 2³ +1 lim 1+1 (x + 1)³

Q: Let f(x)=√√3-x and g(x)=√x²-1 f Find O - 8 - and state its domain -(x) = √3-x

A: Given, f(x)=3-x  and  g(x) = x2-1 To find fgf(x)g(x) = 3-xx2-1

Q: 2. Find the general solution. a) a' = -(2/t)x+t. b) y'+y=e². c) x² + 2tx=e-t² 1. First-Order…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Calculate the derivative. (Use symbolic notation and fractions where needed.) d dx (-9x³ + 4x² - 7x)…

A: Topic - derivative of a function. we are given function:-9x3+4x2-7xand we know thatddxxn=nxn-1

Q: Cost, Revenue, and Profit A company that manufactures sport supplements calculates that its cost C…

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Q: 9. 5 ( 47--1) dy

A: We know that ∫yn dy = yn+1n+1 +c   ; when n≠(-1) If n=(-1) then  ∫1y dy = ln(y) +c      , (Here c is…

Q: 1) lim x² - 16 x 4 x + 4

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Q: Find the general solution of the following equation.

A: Find the general solution of  dy/dx= yex

Q: Solve the following differential equation. 2y""+11y'''+18y"+4y'-8y=0

A: We have differential equating 2y4+11y'''+18y"+4y'-8y=0 Auxiliary equation 2m4+11m3+18m2+4m-8=0 Lets…

Q: Consider the function Compute fx(1, 2) and fy(1, 2) f(x, y) = 3x²y + 5x²y²

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Q: Question Given f(x)= = -2x² + 14x - 12 x-1 Select the correct answer below: I which of the following…

A: Let's solve limit and continuity problem.

Q: f(x) = 6x12, x 5- 2 if x ≤ 2, if x > 2.

A: Consider the function  f(x)=6x-12,     if x≤25-x2        if x>2

Q: The equation of the tangent line to the curve y=3x² - 2x

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Q: Question Given f(x) = -4x³ - 3, use a table to estimate the slope of the tangent line to f at the…

A: Given function : f(x)=−4x3−3 at the point P (-2,29)

Q: Consider the function ab a b |a| g(x) = TT a sin²(x)+1 kx+1 2x+1 a) What is the condition on a in…

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Q: Given the function f(x) = (x² − 9) (x² + 9), the number of horizontal tangents of f is

A: The given function is fx=x2-9x2+9 We have to find number of horizontal tangent line for fx

Q: c) g(t) = = 5t² 3 3 214

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Q: Consider the function g(x) = a sin²(x)+1 kx+1 2x+1 if x T 2

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Q: Question Find the average rate of change of the function f(x) = x² - 8x + 22 on the interval [3, t].…

A: Concept: The average rate of change of the function f(x) at the interval [a, b] A(x)=f(b)-f(a)b-a

Q: 2. Given the vector function (t) = (cos 2t, sin 2t, tan² 2t), find a) The unit tangent vector T (t)…

A: Given question :- We have to find unit tangent vector and equation of tangent line at the given…

Q: Let G(x) = = - 7x + 12 |3 - x| + |x-1| for x = 3.

A: The given function, Gx=x2-7x+123-x+x-1 for x≠3 We have to simplify the function Gx on the interval…

Q: Find the solution r(t) of the differential equation with the given initial condition: r(t) = { r'…

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Q: Comet Brittany-1952 moves along an ellipse with equation 64x²128x +9y2 - 512= 0 (shown below)…

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Q: 121. [T] y = -at (1, -1) 2

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Q: Use the given graph of the function to find the x-values for which f is discontinuous. 1,0 1,0…

A: Topic- Discontinuity of a function A function is discontinuous at a point if there is a jump in the…

Q: Let f(x)=(x+x^-1)^2. Find f'(5).

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Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by…

A: ∫ t lnt+4dt

Q: 4. Ignacio wants to have 10,000 pesos at the end of 10 years. He decided to open a bank account that…

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Q: Q1/ Solve the following first-order differential equations: 1- (1+x³).dy-x² y.dx=0 2- (1+e20)dp+2e²8…

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Q: 5) The equations r² + y²s + yt² - 13 and y² + x²s + rt² = 9 define s and t as implicit Əs functions…

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 8 lim (x, y) (0, 0) x 3 xy…

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Q: 2. Solve each problem : (a) Find an equation of the line that passes through the point (-3, 4, 2)…

A: I have appended the formula used in the solution part

Q: 3. Substance A is being observed and it was recorded that its half-life is 6 months. Determine the…

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Q: 4. 5. cy² = x² + y x = A sin(wt + ß); w a parameter, not to be eliminated

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Q: a. f(x) = √x 2 b. g(x) = √x²

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Q: B. Find the indicated limit if it exists (2x+1 if x <3 if 3 ≤x 1. lim f(x) if f(x) = {10-x

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Q: We are trying to prove the following limit. Once we have specified & in terms of &, one of the steps…

A: From ε-δ definition of limit we know that, limx→af(x)=L implies for a pre-assigned ε&gt;0 there…

Q: 1. For the function y = 5x³ - 4x a. Determine the average rate of change between x₁= 3 and x₂ = 5.…

A: Here we have to find average rate and instantaneous rate of change.

Q: the domain of F is the set of all real numbers except _____, and its range is the set of all he real…

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Q: Given the vector function 7 (t) = (cos 2t, sin 2t, t), find 7(2), Ñ(1), B(4)

A: Given that  r→(t)=cos2t,sin2t,t

Q: Suppose that f and g are continuous functions such that f(1) = 9 and lim[ƒ(x) +6g(x)] = 13. Find x-1…

A: Topic- Limits and continuity if function is continuous at x=c at x=climx→c-f(x)=limx→c+f(x)=f(c) we…

Q: (g) Use V (2) and V ′(2) to estimate the value of V (2.1). (h) Find the maximum number of people…

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Q: Problem 4: Find the set on which the function is continuous. 1 a. f(x) = 2-¹ e b. f(x)=√4x²

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Q: f(t) = 18 h(t) = -2t Evaluate. f(h(-5))=[ Show Calculator Stuck? Review related articles/videos or…

A: Topic = Functions

Q: The graph of y = f(z) is shown in blue. Draw the graph of y = f(2), shown in red, by determining how…

A: Given Graph:-

Q: Comet Craig-1959 moves along an ellipse with equation 49x² + 4y² - 196 = 0 (shown below) -10-9-8-7-6…

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Q: Question Find the points at which the following function is discontinuous. 6x²+1 f(x) = -5x -5 if x…

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Q: Set up but do not evaluate the integral to find the length of the arc of the curvey = x = 5 to x =…

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Q: For f(x) = 3 x+3 and g(x)= find a. (fog)(x) b. the domain of fog

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Q: -8 4 0 -4 4 8

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