O b) 5² (enx)'s dx :) (Z) !

Q: dx 3+ x2

A:

Q: M(3, 5) is the midpoint of PP2, where P has coordinates (0, 1). Find the coordinates of P2.

A: M (3,5) is the mid point of P1P2¯ , where P1 has coordinates (0,1).we have to find the coordinates…

Q: QI/ Evaluate: 1-S(y3" + y2n + y")(2y2" + 3 y" + 6)i dy.

A: Proceed as shown below...

Q: Find the convolution between x(t) = 2 rect and h(t) =rect() %3D

A:

Q: er + e-x3 d) k(x)= 3e* + 4x

A: Given function, k(x)=ex+e-x33ex+4x

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

A:

Q: 00 10) evaluate (x + 2)5e-(*+2) dx -2

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Q: If f(x) = (x6 + 4x) ³, then df(x) a) 3(x64x)² (x5 + 4) b) 3(x6 +4x)² Oc) (x6 +4x)² (6x5) da equals…

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Q: :1 S* d(x³). 3

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Q: Exercises: Differentiate the followings 1. y = (2x2 – 4x + 1)60 %3D

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: -1/2 6) xdy+ydx=(x²+y')"/?(xdy-ydx)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

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Q: 4) [ (2– t)/tdt xdx 5) o Jr+ 2x 2

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Q: C4

A: Given, Evaluate ∫ex1+e2xdx

Q: pk Ph (x)=k! T(m-k+1) (k+m+1) m X \x X

A:

Q: The zeros for Ax) = x-4x-9x + 36x are 1) (0,+3,4) 2) (0,3,4) 3) (0,±3,-4) 4) (0,3,-4)

A: Using method of synthetic division to find factors of f(x).

Q: (2) DE (D² D²-70³-11 0²-80-12/9=0

A: A detailed solution is given below.

Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: If n(Ax B) = 620 and n(B) = 31, find n(A). n(A)= n(B)= @)(::;:233)5

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Q: Show that if (B) (C) N N then the value of neither x nor y can exceed 1/4. (A) N = X, 2x, = 3x and…

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Q: 7. (D² + D²)z = a²y²

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Q: (ii) w* +1 – 8(@) TOEY 4 2.

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Q: ) Differentiate: Y(u) = (u-2+u-³)(u³ + 3u?) и и

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Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: Let a bc A= d ef g hi Assuming that det(A) = – 7, find a) Det(2A) b) Det(A´') c) Det(3A') d)…

A: Given that: A=abcdefghiand det(A)=-7

Q: 8. Find y'ifys34-7x+2)+4%-2

A: Differentiation

Q: 2. (D² +9)y=5e" – 162.x

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Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: A Find a numbel z That satisfies The condubion g af The MUT I dx= 9 4 -4 O -a 0-15

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Q: dx 4+e¬*

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: (D² - 4D + 5)y = e¯*; yp a. Yp 10 b. y, =#e* 10 C. y, =e* 10 d. y, =e* 10

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Q: 21 (D² +6D² + 12D+8)) = 0 [AD: y = (C₁+C₂K+ (3²²) ²24

A: Given differential equation D3+6D2+12D+8y=0. The objective is to solve the differential equation.

Q: Yob) a) fog)(x) & 3. = (x)) JI 2. x+2 (x)6 8 %3D then find

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Q: 4 If f(x) = ln(2x² – 3) then f'(x) =? - 2x a) 2x2 – 3 - 4x b) 2x2 – 3 2x c) 2x2 + 3 -4x 2x2 – 3 -…

A: f(x) = ln(2x² - 3) So, f'(x) = 1/(2x²-3) × (2x²-3)' So, f'(x) = 4x/(2x² - 3) .... Option (b)

Q: 2 (b) L1²}=3

A:

Q: 9/Express flx) in the form fCx\=(x-K)q(x) tr for the given value o f k ):子メー5x3 -12x°-X; K3 -5 9.…

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Q: x/2 – x) · (e*² + x) dx = et + C 3

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Q: 64+ 203 - 6D² - 16D -8)y =D

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Q: Ay l Ory"- 8y/ (ry + y) O zyy"=/ (ry + 7y) O ry" - / (8zyy) O zy" =/ (zy - 8y)

A: We will find out the required value.

Q: z 1 dz 54. z(z 4)

A: Partial fraction:

Q: 20 %3D Find (all) the value(s) of c such that 5c2n 3 n=0 (A) c= 2 (B) с — 7 (C) c= -2,2 (D) c = |…

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Q: Ify = 5+5 In x - 2e" dx 5. -2e" O a) 5 + O b) 5 In(1) - 2e O) 5 2xe-1 d) 5 2e" Oe) 5 + 66

A: Given y=5+5*lnx-2*ex so differentiation of y is dy/dx