Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

Q: Find the general solution to: dy X xẩy = xảy x²y d y = o y = Cet² ° y = Cezx² ○ y = ex² ez x² + C…

A: We need to find out the general solution of the differential equation.

Q: find a set of parametric equations of the line through (2,8,3) and (11,20,21)

A: The line through the points (2,8,3) and (11,20,21)

Q: 1. Which of the following is the value of n so that a. 0 b. 1 tan tan"x cos³x dx = c. 2 d. 3 1 sin³x…

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Q: lim f(x) = 5 and_lim_f(x)=5, but f(3) does not exist. X-3 X-3* What can you say about lim f(x)? X-3…

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Q: 9. Solve the differential equation: xy + y'=100x

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Q: Answer the following questions for the function defined on the interval [-5,7). a.) f(x) is concave…

A: Use derivative concept

Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

A: Note: ln(a×b)=ln(a)×ln(b)....(i) ln(an)=n×ln(an) ..........(ii)

Q: Use a sum or difference identity to find the exact value of the expression. tan 75°

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Q: 4. y = 2x + 2 - 2x² + x + 6

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Q: Evaluate fetanx sec² x dx

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Q: Find the radius of convergence, R, of the series. R = 00 Σ n = 1 7 || xn 4n - 1 Find the interval,…

A: We have to find out the interval

Q: 1 n (Inn)3/2 Σ(-1)". n=3

A: Given: Here, an=1n(ln n)3/2≤1n(n)3/2=1n5/2. So, the given series is absolutely convergent by the…

Q: Find the average rate of change for the function over the given interval. y = ex between x = -2 and…

A: topic- average rate of change of function over interval Note: As per bartleby guidelines,we are…

Q: Given sec 8- -13 $ 3 03 N what is cos?

A: Solving the problem by finding the value of Cos.

Q: Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

A: Please see the below picture for detailed solution.

Q: Problem 8. [10 pts] For each of the following answer True or False. If it is false, explain it. (a)…

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Q: Select the correct steps when differentiating from first principles. O a. O b. O C. O d. lim 0+x lim…

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Q: The rate of change of N is proportional to 20 + N(x), where N < −25. N(0) = 10, and N(2) = 25, find…

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Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: find the area of the triangel with verticies A=(0,0,0) B=(2,1,1) C=(3,1,2) round to 2…

A: This question can be solved using the concept of area of triangle using vectors.

Q: Find the radius of convergence, R, of the series. R = Î n = 1 I = n2n Find the interval, I, of…

A: We have to find out interval of convergence

Q: 1 2-4 를 -5 금 dr

A: Since the third question is incomplete, solve first and second integral

Q: 2. A function is said to be if, graphically speaking, you can trace the entire curve without any…

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Q: Use the given substitution to express the given radical expression as a trigonometric function…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Evaluate the following integral. Л √4 sin *x dx 0

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Q: dp dt Suppose that the current population is 100,000. (a) What is the predicted rate of growth 3…

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Q: What is the exact value of sin(-150°)? -|N 1 7개 6 아틀

A: Find out the exact value of the given trigonometric function.

Q: What is the equation of the curve that passes through the point (1, 3) and has a slope of 2 x+3 O 9…

A: Here we have to write the equation of the curve that passes through the point (1,3) and has a slope…

Q: The rate of growth of the population of a city is predicted to be the following, where p is the…

A: topic - differential equation

Q: Find both first partial derivatives. xy x² + y² f(x, y): fx(x, y) = (No Response) fy(x, y) (No…

A: Here we have to find the partial derivative.

Q: Calculate the double integral. 7x S₂ x ² + x²0² +y dA, R= [1, 4] x [0, 1]

A: Explained below

Q: Which of the following functions has an amplitude of 4 and a phase shift of 4 f (x)=4cos 2x- (2x-4)-…

A: Solution

Q: [4x 4x csc (4x) cot (4x) dx =

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Q: (c) State the Fundamental Theorem of Calculus Part II.

A: In this question we have to state the Fundamental Theorem of Calculus Part II.

Q: Find the curvature K of the curve given below. r(t) = ti+8t²j+2tk

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Q: Determine la derivada de ƒ (x) = 5 sec x − √√3 csc x - Llene los blancos (sombreados de azul claro)…

A: I have stated the used formulas in the solution

Q: Find both first partial derivatives. z = exy дz ax əz ду = (No Response) (No Response)

A: The given function, z=exy

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ f(x,y)= fx(x,y)= Of(x,y)= f₂(x, y) =…

A: We need to find partial derivative.

Q: What is the exact value of csc > O 2√5 3 IN O-2 14 (¹4) ²

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: S 4x+1 4x² + 2x + 1 dx In 14x² + 2x +1| + C Option 1 In 14x² + 2x + 1] + C 2 In 1 4x² + 2x +11+ C…

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Q: Prove the identity. 1+ tan 0 1- tan 0 1- tan 0 =0 19: + To verify the identity, start with the left…

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Q: Show your complete solution: Evaluate the triple integral pl+y² xdtdydx 1-x S S T 2y

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Q: y(0) = -1 0 = (0),

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Q: 5. Integrate the function below, if the answer is expressed as (a/b)*pi + 2*In(c), find the value of…

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Q: Evaluate fx and fy at the given point. 5xy f(x, y) = (1, 1) 6x² + 3y²' fx(1, 1) fy(1, 1) = (No…

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Q: Explain whether or not the Quotient Rule should be used to find the partial derivative. Do not…

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Q: ections at the given point

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Q: Let H(x) = f(x) - (x²+5) where f is the function described by its graph below. 3 2 1 0 What is H'…

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