Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the definite integral | f(a* – 20*) · (x³ – æ)dx.

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A: Topic = Derivative

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A: Given problem is solved below.

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Q: 2. x'dy+(2ty– y°l&x =0 Let the substitution y=²; y=vx; dy=vdx+ xdv

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Q: 3) y' dx-(xy+y*) dy-o Let the substitution v= i y vx; dy-vdx+xdv %3D )x*dy+(2xyy*) ax -o Let the sub...

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Q: х - у ·+1 х+у y 2. ||

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Q: Beth is filling a small backyard pool with a garden 647. hose. The pool holds 30 gallons of water. A...

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Q: 1. Find the order and degree of the differential equation: dy +5 dx 4 14 sin x. dxº

A: Given- d9ydx9+5dydx4=14sinx To find- order and degree of given differential equation

Q: 5. ) lim x-0 x +1 x2 +9 (b) lim (7 -2) 1 x2 +9 (c) lim- (d)lim n-00

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Q: y'dx-(xy + y* kty = 0 1. Let the substitution v=2; y= vx; dy = vdx+ xdv

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Q: 1.d) * when x = 0; y" e* + (y') = 5 True O False

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Q: y-x=C1e^x+C2e^2x Eliminate Arbitrary Constant

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Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = t 2 – 3t – 18, w...

A: Given,           Suppose that a particle moves along a straight line with velocity defined by       ...

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A: Given that: Slope at (2, 3) is given by 2x+12y-3

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A: On changing determinant of row to corresponding column, there will be no any change on determinant.s...

Q: x*dy + (2.xy – y² }tx = 0 Let the substitution y=2; y=vx; dy=vdx+ xdv

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Q: . Using inclusion-exclusion find the number of ways to put 9 pairs of people in a ne of 18 so that n...

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Q: (a) y = -T (b) y = 2x° + 3x (c) y = x² + 5x 7 (d) y = x(x - 1) %3D -

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Q: a) a fonction f (x)y) is homogeneous of degree 7 in X and y it and only it, 3 b.) The function f(xy)...

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Q: A// Find the derivative of y with respect to x 5) 3tan-1x + sin-1x = 4 6) y = ln- 1+ ex = la,

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Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

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Q: Z1 = 2 + 4i Z2 = 5e2i Z3 = 4 cis 40°

A: Solution is here

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Q: Evaluate the given limits numerically and graphically:

A: Given that:                            4. limx→39x2-95. limx→3x-3x2-2x-36.limx→-1x-3x2-2x-3

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A: Given: y=x3, y=1, x=0 &amp; x=1 From the given curve the bounded region is as shown below: Apply th...

Q: 2.c) Eliminate the Arbitrary Constants in the equation: * y – x = C1e* + Cze-2* -y" - y + 2y - 2x + ...

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Q: II. Solve the following homogeneous differential equations. 1. y'dx-(xy+ y kdy = 0 Let the substitut...

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Q: Determine the values of x for which the given function is undefined. (Let k be any integer.) y = co...

A: To determine the values of x for which the given function is undefined. y = cot x 

Q: 1. y'dx-(xy + y* \dy = 0 Let the substitution y=2; y= vx; dy=vdx+xdv

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Q: Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x) =...

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Q: Find y''' of: y=4cos(x/2)+3x^2

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Q: EVALUATE THE INTEGRAL OF THE FOLLOWING. INDEFINITE INTEGRALS. CLEAR

A: We will find the integral's value. 

Q: A function F is an antiderivative of the function f on an interval I ifLfor all x e 1. (A) F(x) =f (...

A: A function F is an antiderivative of the function f on an interval I if 

Q: 23. Solve for x: 3ax-1=4 24. Solve for x: 3ax-4a =7+3ax 25. Solve for x: 3ar-4ax =7+3a

A: As we know from the fraction rule: a-b=-ab 23). Given: 3ax-1=4  ...(1)  

Q: 40 . Find the sum 2 (2k + 3) , arithmetic sequenc, use S k=1

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Q: y'dx- (gy + y* }ty = 0 1. Let the substitution v=2; y= vx; dy=vdx + xdv

A: We have to find solution of given differential equation.