Evaluate O O O O e e+1 2 e+1 In eftdz. S et +1 In e+1 2 1 2 1 2

Q: let cosx=-4/5, pi<2<3pi/2. find csc(x/2).

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A: Answer :   Critical point : x = 0.193π and increasing in nature.

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Q: s) Given the piecewise function below, find h(-5) and h(-4). if x < -4 h(x) = { 6x - 7 √x+8 ifx ≥-4…

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Q: Given f''(x) = 4x + 5 and f'(-1) = 1 and f(− 1) = - 1. Find f'(x) = and find f(4)

A: Let's find function and it's value.

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Q: 2. S (4x+5) x²+4x+20 dx

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Q: Use the rules for sums of powers of integers to compute the sum. 22 [² j=8

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Q: Onsider the function f(x) = -4x²+7x+6. Interpret the e average rate of change from x = -7 to x = 7…

A: Topic:- application of calculus        Definition :-  The tangent represents the instantaneous rate…

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Q: Solve the following inequality: 2x + 4 8 x < 16 x < 10 x < 8

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Q: Consider the function f(t) = 6 sec²(t) - 6t³. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: The given function is: ft=6sec2t-6t3   As we know that; The expression for the antiderivative:…

Q: 2 y²dx + xydy = 0

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Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

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A: Maclaurin series is given by:

Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Find the Fourier series for the following functions: f(t) = |sin t], -1 < t < n and The function is…

A: Solution is given below:

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Q: • 25 Which of the following graphs represents (+2 30 la T 7 17 T 49 19 15 O . 7 17 T 19 19 15 19 19…

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Q: Which one of the following equations could work for the following graph? y = 5 y = -5…

A: To find,  the equations could work for the given graph.

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Q: Find (4x + 2x³) dx

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Q: IV. Fill in the blank to make each statement true. Use correct notations. 2. If ƒ(x) = 1 – log5 x,…

A: The objective is to find inverse of f.

Q: Evaluate the following antiderivative/indefinite integral: / [(5x² + ² + + 50² + 7) de 36 X x3 k:…

A: Topic:- application of integration

Q: ical numbers r = -1 and x = 2 are found from a continuous derivative the second derivative is f"(x)…

A: Topic:- application of derivatives

Q: Evaluate the following limit: lim+1 x+1 01 2 02 Oc undefined

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Q: Consider the smooth parametric curve defined by the equations t (t²-3) { = = 3 (t² - 3)' = where t E…

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Q: An estimate of ³₁x¹dx using Simpson's rule with n = 4 gives a. 242/5 b.244/5 c. 148/5 d. 152/5

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors

A: Given So we do partial fraction to get Distinct linear factor and Repeated liner factor

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Q: Which equation represents a line that goes through the points (0, 1) and (1, 0)? y = -(x + 1) y = 1…

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Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: Use the graph of y = f(x) for problems 7 and 8. 1010 lim f(x) = 1; HI-4+ lim f(x) = 1; 41144 Use the…

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Q: "풍 2 secx dx tan³x + 4 tanx

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

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Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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Q: Which of the following equations represents a line that passes through the point (0, 1) and has a…

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Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

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