Use integration, the Direct Comparison Test, or the Limit Comparison Test han one method applies, use whatever method you prefer. dx 8 , O

Q: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 5, g'(2) = 3, and f(3) = 6. Find r'(1).…

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Q: Evaluate the integral using partial fraction method J (3x²+2) dx (x + 2) (x² + 4)

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Q: Find an equation of the line that goes through the points (-3,-18) and (3,12). Write your answer in…

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Q: Find dy/dx. y = log(sin2x)

A: Given Function is as follows As we know that

Q: Year Percent 1975 56 1980 59 1985 58 1990 70 1995 76 2000 2004 88 89 Let f(t) be the capacity (in…

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Q: Find y" by implicit differentiation. Simplify where possible. x² + 6y² = 6 ||

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Q: lim x-1 sin (x-1) x²-1 =

A: (2) L=limx→1sin⁡(x−1)x2−1

Q: Find the derivative of the function. y = cot² (sin 8) ||

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Q: Find a) any critical values and b) any relative extrema. f(x) = x² - 2x + 5 OA. The critical…

A: to evaluate critical value and relatives extreme of the function f(x) =x^2-2x+5

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x² + xy +…

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Q: Find the area of the region bounded to the right by x = -2y and to the left by x = y². 2- + 543-2 3…

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Q: Let f(x) = 3(x-6) 2/3 + 2. (a) Find the interval(s) where f(x) is increasing. (Enter your answer…

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Q: Answer the following True or False. [6³dx = da 6 + C In 6 O True O False

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Q: When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes a 20°C room…

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Q: Find d2y/dx2 by implicit differentiation. y + sin y = x

A: To Find d2y/dx2 by implicit differentiation.y + sin y = x

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(3) and G'(3). F'(3) G'(3) = = f(3) =…

A: Given,  F(x)=f(f(x)) and .Given, f(3)=9, f(9)=3, f'(9)=4, f'(3)=15

Q: Use the given graphs of the function f (left, in blue) and g (right, in red) to find the following…

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Q: Determine the appropriate f(x) and a, and evaluate L(x) = f(a) + f'(a)(x − a). (0.98)3 Calculate the…

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Q: Problems 3-7, use derivatives to find the critical points and inflection points. f(x) = x³-9x² +24x…

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Q: conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. If water…

A: A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high.so r= 10ft…

Q: If xy + 5ev = 5e, find the value of y" at the point where x = 0. y" =

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Q: A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

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Q: 6. Find the sine and cosine of the angle that the point (3/5, 4/5) on the unit circle makes with the…

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Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. 3 f(x) =…

A: we need to find out the intervals where the function is increasing and the interval where the…

Q: (a) f(0) = ln(sin 0) + sin(ln €). (c) y = ln |x³ — x²| (b) f(x) = log₁0(1 + cos x) ax In (a + x) (d)…

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Q: Find the RREF of the matrix 2 3 12 -2 22 -2

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Q: If ƒ"(x) = x²(x − 3)(x + 5)³ then ƒ(x) has a point of inflection at Select one: a. x = -5₂ x = 0 and…

A: given

Q: The width of a rectangle is 7 less than twice its length. If the area of the rectangle is 141 cm²,…

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Q: 1. (x²+y²)dx+xy dy=0

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Q1. Let f(x, y) = x²y + x + y² +3. (a). Find f(x, y). (b). Find dy

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Q: Draw and label a diagram to help solve the related-rates problem. The side of a cube increases at a…

A: We consider a cube on each side is x m long.Draw a cube and mark its length, width and height as x m…

Q: A chain of mass M and length L is suspended vertically with its lower end touching a scale. The…

A: We have to find the reading on the scale when the length x of the chain has fallen.

Q: Solve the following differential equations: 2- ex+²ydy - e¹-2x dx = 0

A: given differential equation

Q: Can we solve this without the Apply L'Hopital's rule.

A: Yes, we can solve this without using L'Hospital's rule.But we need some standard formula.

Q: 21. xy = 7; (1,7)

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Q: Based on the graph of g"(x) pictured above, how many points of inflection exist for the twice…

A: As we know The inflection point exists when  and conavity changes  of function

Q: Consider the points P = (1,1) and Q=(3,-1). (a) Draw the points P and Q and draw an arrow from P to…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 5xy - 4x² -…

A: We are given a function and we need to find out the relative maximum, minimum or saddle points if…

Q: Determine whether the series is convergent or divergent by expressing s as a telescoping sum. If it…

A: A telescoping series is a series in which all the terms in the middle are cancelled except for the…

Q: An aircraft is flying at a constant altitude with a constant speed of 600 mi/h. An antiaircraft…

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Q: Find the inverse of the matrix B = B-1 = ab sin (a) Use B x = 1 di sin (a) f to solve BT 8 f ?х = 8…

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Q: Find the four second partial derivatives of f(x, y) = 7x+4y7 +6x6y5. 224 2

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Q: Find the zeros of the function and state the multiplicities. 2 n(x) = -6x³-39x² - 60x If there is…

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Q: Find the derivative of the function. 1 + x 1- x y' = y = arctan

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Q: Find the derivative of y = x².

A: y = xx

Q: Differentiate. h'(0) = h(0) = 0² sin(0)

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Q: 0 1 √ √(x²+2x+1) dx

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 10-- 8 4 2 y 8 ► » -2 2 4 6 8 10

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Q: Suppose that z = x³ x³y², where both x and y are changing with time. At a certain instant when x = 2…

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Q: A student takes out a college loan of $4000 at an annual percentage rate of 4%, compounded monthly.…

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