Write the expression as a sum and/or difference of logarithms. Express powers as factors. In (x1¹²√7-x).0

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A: F′(x)=f(x)=6e2x and F(0)=4

Q: 7. Evaluate the definite integral. a. b. С. 9 cos(xt/2) dt в'ітетка 1+ * = dx 47 dx

A: The given intergals are

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Q: Evaluate the following improper integral. So e 0 e-bt sin (at)dt, where b=2, a=1 Round your answer…

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Q: To check for the result, you have to prove that + C] = 8⁹. + sec²0. d 1 10 de Evaluate the left side…

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Q: Please do part a)

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Q: 1. Find the area bounded by x = y²; x = −2y² +3

A: To find the area bounded by

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Q: Find the arc length of the graph of (y − 1)3 = x2 on the interval [0, 8]

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Q: 6. 14 ) Consider both geometric series below. 3 SA = 00 Σ n=1 5n and SB = M8 n=0 3 5n Both SA and SB…

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Q: Solve the following Initial Value Problem. dy dt - y= sec² (t) + 3 sin(t), y() = 1

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Q: Find the area of the region enclosed by the curves between their intersections. y=x² and y= 2x

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Q: 2) Find S -18 dx

A: The given integral is e1/x.

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: Ĵ Refer to the graph shown below to evaluate -2 fit) f(t)dt.

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Q: 0 1 2x (4 – x²) dx

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Q: 5. If f(5) = 7.8 and ƒ' (5) = 5.2, then use the linear approximation (also called the tangent line…

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A: The given graph of f

Q: x3 x² + 4x +3 Example: ₁ dx

A: We have to perform the partial fractions

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A: The given integral  where R is the trapezoidal region with vertices

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A: the series is: the sum from k=1 to infinity of 1/(16k2 - 4)

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

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Q: Find the average rate of change between x = 1 and x = 5 for the function shown in the table below. X…

A: x−5−4−3−2−1012345f(x)4734231472−1−2−127Average rate of change of f(x) on [a,b] is Average rate of…

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Q: Find an antiderivative of the function g(x) = 6x³ +7. An antiderivative is

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Q: (c) (d) (e) creasing? Does g(x) have any critical points? If any, identify all critical points. On…

A: Given: To Find: (c) To find the critical points if any of g(x).(d) To find the interval(s) on which…

Q: Given the definitions of f(x) and g(x) below, find the value of (fog)(2). f(x) g(x) = X = -x+ 2 2 _…

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Q: (1) Let C₁ and C₂ be arbitrary constants. The general solution to the homogeneous differential…

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Q: Consider the following. f(x) = 48x − 4x2 Find  f '(x). f '(x) =        Find the critical…

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Q: Find the indefinite integral. x¹ + 24 dx = +C

A: Let,

Q: ∞ 4. Apply the Ratio Test to the series [ the limit lim n→∞ (3n)! n=12¹ (n!)3 an+1 an and find

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Q: Find the integral. Use C for the constant of integration. | cv² (y² + 3)² dy

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Q: Problem 2. (Fundamental Theorem of Line Integrals) Suppose that the curve c connects the point (0,…

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