20 of 21 What is the average rate of change of y with respect to x over the interval -5, –2] for the function y = 3x+2? 3 O -9 O -1

Q: f(0) = –3, f' (0) = –15, f"(0) = –3, f"'(0): f(x) = +..

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Q: 1 Evaluate the limits 1im - x+2 X* 1/4 1/2

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Q: Problem #2: Differentiate f(x) = [(6x³ – 3)(7x² + 8x – 1)]° and solve f'(2). %3D Solution: Reason:

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Q: } Consider the initial-value Question 2 ( problem y" + 4y = 5 sin 3t, y(0) = 0, y(0) = 3. (a) Use…

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Q: On the circle x² + y² = r², find y". r2 A. y" C. y" = y - x3 E. None of these -x² - y2 В. у" D. y" :…

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Q: 15 Evaluate. 2n - 1, where n = 6 1 32 63

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Q: The general solution of the fourth-order differential equation y() + y" + y" =0 is: %3D y=c_1 +c_2…

A: The general solution of the fourth-order differential equation.

Q: Question 2 ( Consider the function f(x)% = %3D a2+1 (a) Find the intercepts of the graph of f (if…

A: Given that      f(x) = x/(x2+1)

Q: Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity…

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Q: 1. Consider the point in the plane whose Cartesian coordinates are (x, y) = (-10, 24). 1.1. Find…

A: From cartesian to polar coordinates we have the following conversion formulax2+y2=r2 i.e.,…

Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost the…

Q: If log, (5x + 6) = 5, then x = You may enter the exact value or round to 4 decimal places. > Next…

A: We will solve for x.

Q: What are the coordinates of the point on the graph of Ax) = (x+ 1)(x+ 2) at which the tangent is…

A: solution:-f(x)=x+1x+2      =x2+3x+2slope of tangent=ddxf(x)                             =ddxx2+3x+2…

Q: In how many ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table? 24 12 20

A: We have to tell number of ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table…

Q: The maximum value of x + y + z subject to the constraint x² + y² + z² = 1 is Write in decimal form…

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Q: The solution of the Ordinary Differential Equation 4y" - y' - 3y = 0 if y(0) O and y'(0) %3| 7 - is:…

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Q: Given that f (x) = x 2 - 5x + 6, evaluate the function f(6). 0 -12 12

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Q: Find the general solution to the trigonometric equation (2 cose - 1)(tane + 1) = 0 function value,…

A: Given equation, (2cosθ - 1) (tanθ+1) = 0 To be found : general solution of given equation

Q: For some constant a, the following improper integral a | (x² + 1)e2×dx

A: We have to solve given improper integration

Q: x*dy tly' txy) (y+xy)dx =0 3-

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Q: (zxャy)dx->xy dy =。 2-

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Q: Evaluate the limits lim x² + 3x- 4. x→-1 -6 -7 -2

A: We can find the limit as below.

Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

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Q: Suppose that f (x, y) has continuous second-order partial derivatives everywhere and that the origin…

A: Given a function f(x,y)

Q: Q2: Determine the type of the two lines (parallel, perpendicular, intersecting, north) and give the…

A: here figure 1  is pependicular line because given that both intersect at 90 degree    in figure 2 is…

Q: Kyle wants to build a rectangular pen for his animals. One side of the pen will be against the barn;…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b). If the…

A: We have to check if Mean value theorem can be applied or not.

Q: Using decomposition into partial fractions, 4x2 + 2 J x(x² + 2) is equal to

A: We can solve this as follows:

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Evaluate the integral by making an appropriate change of variables.   7(x + y) ex2 − y2 dA,…

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Q: Given y, (x) = x? is solution for the differential equation x²y"-3xy' +4y= 0 Using the reduction of…

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Q: |Q1/ Find the transpose for A(3×4) matrix. Q2/ Add two (2×2) matrices and put result into new…

A: We have to find A' and A+B

Q: (x + y) dx dy dz =? Select one: 9. O 1 O 5 None of them

A: Topic = Integration

Q: Determine s) for $) = 31 + 212 1 s'() = 41 + 3 Os') = 41 + O s'() = 41 - %3D s'(t) = t+4t %3D

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Q: 5 Find the eigenvalues of the matrix A = 2 -8 -8 = Enter both values separated by a comma.

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Q: 1. f(г) — 2? + Зх — 6, д(х) %3 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: degrees

A: We will find the degree of freedom.

Q: By writing the summation of the two power seriesE 2nc, x"+ E 6c,x* 0, we obtain: Ze + o[2(k + 1)ces…

A: We have: ∑n=1∞2ncnxn-1+∑n=1∞6ncnxn+1=0...(1)

Q: testonvergence and divergene h.

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Q: 4 Find f(x) dx if if x< 2 f(x) if x 2 2.

A: To evaluate the given integral

Q: 7. Lonsider the plane through the three polnts Po(1, 0, 0), Pi(1, 1, 0), P2(0, 1, 1). 7.1. Find an…

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Q: If 30,000 cm2 of material is available to make a box with a square base and an open top, find the…

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Q: Using decomposition into partial fractio 2x2 + 2 x(x2 + 2) is equal to

A: We have to find solutions

Q: 3) [- y" + 3y - 4y = 20, | Given the IVP: У(0) %3D 0, у(0) %3D —5. A) Use the Laplace transform to…

A: Solving

Q: * the differential equation (x+y)dy+xdx=o is Homogeneous equation None of the above exact equation…

A: A detailed solution is given below.

Q: Problem #2: Differentiate f(x) = [(3x* – 5)(2x³ + 9x – 6)]° and solve f '(2). Solution: Reason:

A: Solve the following

Q: What is the solution of D.E y"- 2y' = e*sinx when solved using the method of undetermined…

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Q: Test the series for convergence or divergence. (If the quantity diverges, enter DIVERGES.) (-1)"-1…

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Q: 2- A hot-air balloon is moving vertically up and down so that its height relative to the ground is…

A: We have to find the velocity and acceleration.

Q: Problem #2: Differentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2). %3D Solution: Reason:

A: To differentiate the given function.