dx 35. Let I = Vx2 – 4x + 8 (a) Complete the square to show that x² – 4x + 8 = (x – 2)² + 4. (b) Use the substitution u = x – 2 to show that I= du Evaluate the u-integral. 1² + 2² (c) Show that I = In V(x – 2)2 + 4+x – 2 + C. 2| + c.

Q: P(r) = 3x – 3r² + 2xr³. Consider the polynomial . Determine the value of P'(9).

A: Solution :-

Q: H.w Exl Let f(x)= 4x+2X+243and go)=3x+3x+3xx +4, where 2. t. f(x),900€75LX] Compute POX) +g (x).and…

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A: To find out the antiderivative we use u- substitution method

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Q: Find f. r0 - VD + Sx), 1) -9 X) =

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Q: (c) Write (V3+ i)" in the form of x+ iy.

A: Here I have applied De Moivre's Theorem. See the solution.

Q: d given the following: Sy = u² + 6u – 2 u = 4x² + 8x +1 %3D

A:

Q: a2f ду? 1 If f(x, y, z) = - 2+y² + find ax2 az2

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Q: メ Find dy S-3xメ+)X-2) (x211) (2X+3)

A: We have to find the derivative of y

Q: Use Cramer's rule find yhe solution of x1: 2x1+X2-3x3=0 4x1+5x2+X3=8 -2x1-x+4x3=2

A: write the matrix D from the given equations  D=21-3451-2-14 calculate the determinant D…

Q: ntegrate: 16x³ + 64x² 7x +41 16x² +9

A: ∫-16x3+64x2-7x+4116x2+9dx Lets first divide using long division.

Q: is f(x) = -3x + 4 a bijection?

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Q: Determine the constants a and b so that x = -1 is a zero point to q (x) = x5-3bx3 + ax2-ax + b with…

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Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: for z = In(2® + y*). Find

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Q: h = (-6x³ + 9xª + 5x7) (7 + 5x – 4x?). Then h= fgwhere %3D f = and g = Using the product rule h'(x)…

A: differentiate this with product rule.

Q: If x? – 2x – 3 = (x+ A)² – B² , then the value of Bis %3|

A: Given that   x2-2x-3=(x+A)2-B2,  we have to find the value of B. To solve the problem we first…

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Q: R= {(x,y) | X is the sister of y}

A: This is question of algebra Here set is given We have to find components of it Further calculation…

Q: Find | |- •√√√√ V 5x ry sin(x² + y2) dedy

A: ∫02π3∫05π3xysinx2+y2dxdy

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A: Given function is gz=z13+z4+2z2+1. We have to find the number of zeroes of gz in the first quadrant…

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A: Topic = Integration

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Q: Find √ √ (4x + 5y)dA where D = {(x, y) | x² + y² ≤ 9, x ≥ 0}

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Q: Evaluate dxdy √√3x + 4y over the rectangle [0,3] × [0,4].

A: We find required integral by using Fubinis method.

Q: Find the constants c0, c1, and x1 so that the quadrature formula Z 1 0 f(x)dx = c0f(0) + c1f(x1),…

A: Consider the given quadrature formula, ∫01fxdx=c0f0+c1fx1 here we need to determine the constants…

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Q: Please help evaluate

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