Making a suitable change of variable and modifying accordingly the limits of integration, calculate the following integral: 1₁²√33 x² 3x - 5 dx

Q: Determine the points at which the graph of the function has a horizontal tangent line. x² f(x) x-3…

A: Given:      fx=x2x-3 A point on a function will have a horizontal tangent line where the first…

Q: A differentiable function f has only one critical number at x = 5. What can we say about this point…

A: If first derivative is negative on left side of critical point and positive on right side, then it…

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Q: Find the critical numbers of the function. f(x) = 7x² - 4x Step 1 To find the critical numbers of f,…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the derivative of the function by the limit process. f(x) - f'(x) =

A: The given function is f(x)=4x2We have to find the derivative of f(x).

Q: 5) Evaluate the function: f(x+ Ax)-f(x) Ax for f(x) = 3x²

A: I have stated the used formula in the solution

Q: (x-4) dx 2 x²+x-6

A: We can evaluate the given integral by using the partial fraction method.

Q: Write the first-order differential equation in standard form. (Use yp for y'.) −xy' = (8x + 7)y +…

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Q: 2. Find f f'(x) = (x + 1)/√x f(1) = 5.

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Q: 3. Find a power series representation d 1 Hint: use - [In(x + 1)] x+1 dx for f(x) = ln(1 + x) and…

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Q: Problem #3: Consider the following statements. (1) Σ n=0 (-1)" 2n+1 X² (2n + 1)! = X- ∞ (iii) The…

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Q: The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 9,…

A: We have to find the 46th term of given sequence.

Q: Graph the function by setting the x-intercept and the asymptote. Provide your answer below: f(x) z 4…

A: We need to graph the function.

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 1 + est L{f(t)}

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Q: nition 7.1.1. DEFINITION 7.1.1 Laplace Transform et f be a function defined for t > 0. Then the…

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Q: Consider the following function and point. f(x) = f'(x) = (a) Find the derivative of the function.…

A: We need to fill in the blanks.

Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: In (x) Find the area of the region enclosed by the graphs of y = 2x (Use symbolic notation and…

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Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

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Q: 5. A. undefined B. 2 × 2 Consider (a) What is the size of QTP-¹? P= A. -1.5 B. -2 = [1 C. 2 × 4 D. 4…

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Q: Evaluate the integral using the following values. [x³ dx = 320, ["x dx = 15, ["dx-4 = dx

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Q: Consider the function f(x) = ($) ². a. Find the inverse of f(x). b. Explain why the inverse is not a…

A: Solution is given below:

Q: a. Let f(x) = sin(x). Find the Taylor polynomials up through order four of f cen- tered at x = .…

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: To find the inverse Laplace transform.

Q: M                   dy/dx - y = e^x y^2

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Q: Find the total area enclosed between y = x³ and y = x over the interval [-1,9]. NOTE: Enter the…

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Q: ds" Evaluate the given Laplace transform. (Write your answer as a function of s.) L{te-15t}

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Q: f(x) = 4x³15x² 18x+6

A: Here we have to find domain of function,1st derivative of function and critical point .

Q: (1) f (1) x²(x³ +1)5 (x³ − 1)5 dx -

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Q: Let A(x) = =f(1) dt for f(x) in the following figure. 3 1 y = f(x) +2 3 4

A: The given problem is solved below in detail. The last part as requested is solved in detail.

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Q: Prob. 6 (a) 3) Find the critical numbers of the function y = x³/2 - 4x¹/2 3

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Q: 1. (a) First find the following indefinite integral A. e666 B. 2e667 (e - 1) e√x+666 [= √x dx = (b)…

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Q: 2x-4 x²-4x+3 1. Express the function f(x) fractions. Find the interval of convergence. = as the sum…

A: Here, the given function is: f(x)=2x-4x2-4x+3

Q: Describe the x-values at which the function is differentiable. x² x²-9 y = y T

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Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy² = 2y + 1,…

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Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: 4) Find the equation of the line (slope-intercept form) passing through (-1, 3) and a) Parallel to…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Follow the procedure given below.

Q: 2. (a) If z = 1+ 3i and v = −2 − i then 1 A. + 2 B. Tin Tin + C. A. 2√6 e-in/6 B. 2√3 e-in/3 D. 2 10…

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Q: ܐ [ xdx x2 -5x+6 A. 3nx-3-2nz-2 +c B. 3ng+3+ 2nx-2 +c C._2n+ 3-3m|x-2+c D. 2n|x-3-3n-2 +c

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Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

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Q: Problem 2: The point P(0.5, 0) lies on the curve y = cos T.I. (a) If Q is the point (r, cos .r),…

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Q: VOLUMES OF REVOLUTION 1. Find the volume generated by revolving the area enclosed by the curve 4y² =…

A: Let's find volume of solid.

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: fx and gxare integrable on the closed interval a,b and k is the constant. we have to find the false…

Q: find the angle between the pair of vectors to the nearest tenth degree 7i-5j,2i-8j

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Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 2y = e-2t, y(0) = 4 y(t) =

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Q: ) . Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =

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Q: Find the centroid of the given region. [Give exact answer in fraction form.] The centroid is ( ).…

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