x +1 Evaluate the given limit of lim if it exists. 2→-1 x4 – 1 O limit does not exist 4 O -1

Q: Find the area bounded by tHe curves y=8x-x and y= 3x

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Q: 9. (Trigonometric Substitution) Let x = 2 sin(0) for 0 < 0 < . Write v4 – x2 as a trigonometric…

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Q: 5sin e Cose de Sin? o +3 Sine -4 2.

A: Solve the following

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Q: If f(-x)=(2,-1), what are the coordinates of f^(x)?

A: Given that,  f-x=2,-1

Q: 11. Rules of Definite Integrals: I f(x)dx = 6, and "f(x)dx = 4 , find the following: a) c)

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Q: Evaluate the integral. 2 dt 1- t2 V

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Q: 25 18 f(x)dx f(2)dæ = / f(x)dx - 10 where a = and b =

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Q: Find fr(x, y) and fy(x, y) given f(, y) = (csc y) Arcsin(x²). %3D

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Q: Only pose the triple integral that calculates the volume of the solid bounded by the surface y2…

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Q: Consider the function below. Use it to evaluate each of the following expressions. (If an expression…

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Q: Find the area bounded by y = x + 4 and y = x2 - 2.

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Q: (b) А — В (с) 2A (d) 2A – 5B

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Q: Use a graph to determine whether the given function is continuous on its domain. [3 – x if x 3…

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Q: 25. Find the intersection of the line [x, y, 2] = [1,4, – 2] + 1(1, – 1,3] and the plane 2r – 4y +…

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Q: Consider the two series: 6n (a) > 5n + 39 n=1 1 (b) n2 In n n=1 Which of the following statements is…

A: Use roots test for checking the convergence  of the series .

Q: +, ×

A: Given problem:-

Q: 3 If f(2) - 8, and f'(2) 4 - 1 Let f'(x) be the inverse function of f(x). (f-1)'( - 8) = - 1 Write…

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Q: Find the derivative of the function. 4 - 4x – x2 f(x) x2 - 6 — 4х — 2 - -1+ f'(x) = -x – 6

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Q: Find the area of the reglon bounded by the graphs of the equations. y = -x+ Bx, y = 0

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Q: 1) Find the first 8 terms of the recursive sequence. =-3 2,a

A: The given recursive sequence is;  an=an-1 - an-2.

Q: Find the sum of the convergent series. 6 Σ 9n2 + 3n – 2 n = 1

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Q: ider the function f(x) = 3 – 72² on the interval [- 6, 7]. Find the average or mean slope of th cion…

A: We wil use the mean value theorem.

Q: Problem 4: Use theorems on limits (limit laws) EXCEPT for the polynomial function rule, to get the…

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/ō-definition of the derivative to prove that f(2) =9.

A: given :f(x)=4x2-7x

Q: cos(x ) + æ5.1 dx. )ln(1+x² 3 cos(x Evaluate 1+ el.61x – 68 - 3. answer

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Q: Convert the differential equation x''' = x'' – 2x' – 4x +t into a system of first order equations by…

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Q: Use part I of the Fundamental Theorem of Calculus to find each derivative, given the following f(x):…

A: On solving this we will get

Q: A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms…

A: Follow next step

Q: Find (3+2) - 2i . 406 754 386

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Q: Evaluate the definite integral by the limit definition. Step 1 To find the definite integral 9 dy by…

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Q: d the area of the region bounded by the curves y = 3x and y = x².

A: Given query is to find area bounded by the curves.

Q: Consider the function f(t) : 8 sec-(t) – 10t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: Topic = Anti derivative

Q: Find the exact value using a sum or a difference identity. SHOW ALL WORK– include the formula,…

A: cos(225°) here 225° = 180°+45° cos(225°) = cos(180°+45°) cosθ is negative in the 3rd quadrant since…

Q: E. Find the value of D, E, and F of the following circle that passes through (-1, 4)(3,2) and (5,2)

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Q: Q1/ Solve the initial value problem (IVP) of the differential equation by using the appropriate…

A: Initial value problem: An initial value problem (IVP) in multivariable calculus is an ordinary…

Q: Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of…

A: Use area concept of integral

Q: ng Part I of the Fundamental Theorem of Calculus, evaluate: da t'dt =

A: Given query is to find the derivative of the expression.

Q: This exercise uses the population growth model. A certain culture of the bacterium Streptococcus A…

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Q: リ=ー"-4), find a) The x-intercept and the y-intercept b) The interval where the function is…

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Q: 5) Find cos (20) if tan @) =Ž and e is in quadrant 3.

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Q: 1 -dx is The value of

A: ∫ xn dx = xn+1n+1+C .

Q: D. Verify if The relatum O y= xe' y= eco{ 2x) is a soluhon to yl-Gy'+13y=D0 is a solution to yl -…

A: For verification of the solution will find the respective derivative and substitute into the…

Q: 1. Sketch the graph of each function in [0, 27n) by transforming its parent function. (a) y = cos(x)…

A: By using the online available graph plotter we will graph the each function in [0,2pi).  As per…

Q: Consider the following series. n In(n) n = 2 Does the function f(x) satisfy the conditions of the…

A: This is a problem related to series and sum calculation. By evaluating integral we will answer the…

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A: Given ,  Two cars are initially 1200 miles apart  At the same time Car A starts driving at 35 mph to…

Q: Evaluate the definite Integral by the limit definition. Step 1 To find the definite Integral dx by…

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Q: Use sigma notation to wrte the sum. 7n Σ

A: Solve the following

Q: 3. Determine the exact values of the trigonometric functions using the given unit circle below. (a)…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3z F(x) = | cos (t°) dt.…

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