1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a relative maximum?

Q: 2/2 2 sin³(x) dx

A: Here is the solution of the given problem.  To solve the problem we use the following formula:…

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Q: Find the first four derivatives of the following functions: 1. y = 4x³ + 12x² + 7x 2. y = 2x5 + 6x²…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (t+ At)² -4 (t+At)…

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Q: C

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Q: Find y': y = cot 0 sin 0 O sin² 0 1-tan²0 O1+sin² 0 cos³0 O-1-cos² e sin³0 3

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Q: Differentiate the function with respect to the independent variable. x f(x) = 4x cos+ + cos f'(x) =…

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Q: Which of the following functions is entire? For each, justify. f(z) = (x² - y²) - 2xyi

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Q: A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the…

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Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: (2x-1)dx 2x³-x²-27x + 30

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Q: Find the interval of convergence of (x - 2)" In (5n) n=2 (Use symbolic notation and fractions where…

A: To find interval of convergence of ∑n=2∞ (x−2)nln⁡(5n) Let an = ∑n=2∞ (x−2)nln⁡(5n) Therefore, an+1…

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Q: 6 1-x² dx

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Q: Q3) Use the integration method, and find the centroid of the shaded area in terms of a and b. y y =…

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Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: Find the volume of the solid generated if the area bounded by y = x² and y = x5 is rotated by the…

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Q: Use - -1-1(x Let f(x) = 9x +7 In (x+1), x>-1. Find - dx (Simplify your answer.) x=0 to find the…

A: By using ddxf-1x=1f'f-1x to find the derivative of the inverse at the indicated point. Let fx=9x+7…

Q: Consider the function f(x) = 4 - 5x², −5 ≤ x ≤ 1. The absolute maximum value is and this occurs at x…

A: The given function is: f(x)=4-5x2 To find the absolute maximum and minimum of the function on -5≤x≤1

Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 20 cm. Answer:…

A: Find area of largest rectangle that can be inscribed in a circle.of radius 20cm

Q: f(x)=0.2+25x-200x² +675x³-900x¹ +400x³ a=0 ve b=0.8 a.) find the integral by using Simpson 3/8 Rule…

A: Concept: Simpson's rule: One of the numerical approaches for evaluating the definite integral is…

Q: 8. y=x²³²₁ x=2, x-axis; about the y-axis ४.

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Q: 8 1 ₁ }(s) = = nº n=1 Show that finding the value of the Reiman Zeta for (2) is just the value Basel…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: Which of these series, if either, diverges? ∞ - 1)k 1. II. Σ(-1)^ (77) K²+1 k=1 k k=1 A. I only B.…

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Q: The function f(x) 2x³ + 42x² = one local minimum and one local maximum. This function has a local…

A: You must have an idea how to use derivatives to find the local maximum and minimum using critical…

Q: T Express the surface area of the surface obtained by rotating the graph of y = 4 sin (x) for 0 ≤ x…

A: Recall: Surface area SA=∫ab2πy1+dydx2dx We have, y=4sin(x), a=0, b=π6

Q: A 200-g sample of a radioctive substance is placed in a chamber to be tested. After 3 h, 140 g of…

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Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

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Q: Determine whether or not the following limits exist (explain why or why not): x² - y² a) lim…

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Q: 17. The general solution of the equation (x³ + 3xy²)dx + (3x²y+y³)dy = 0 is A. (x4 + 6x²y² + y4) = C…

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Q: How many square units is the area enclosed by y + 2x - 5 = 0, y = 4x - x² and x² - 4y = 0 ?

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Q: Find the partial derivatives of the following function: z = f(x, y) = e¹²¹² fx= fxx = fxy = fy= fy=…

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Q: Evaluate the following limit using L'Hospital's rule. Provide your answer below: lim (3x6) sin = 818…

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Q: se the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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Q: along the line AM WI a magnitude of midpoint of the vertical side OB of the parallelepipe Express F…

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Q: For the following integral, reverse the order of integration and evaluate the integral. 1/8 1/2 S S…

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Q: The graph of the function f(x) is shown below. At which point(s) is f not differentiable? At which…

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Q: 1. f(x) = x² − 16x, [3, 10] 2. f(x) = 15 – 2x − 2x², [1, 2] 3. f(x) = 2x³ + 3x² − 12x + 24, [−4, 0]

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Q: Find the normal line to f(x) = ax² - 4ax at x = 3. Assume that a is a positive constant. Next…

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Q: Compute the following limit. 1-cos(z) as x approaches 0

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Q: Given f(x,y)= x³(x²y³-2y²), find all of the first and second partial derivatives.

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Q: Show that the operators T and T₂ from 2 R² into R² de fined by T₁: (F₁) √₂ ) → (9₂9₁) and T2=…

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