It is given that 1 (x+3)(x+1) the Fundamental have / 2(x+2) (x+3)²(x+1)² * Theorem of Calculus, we 1 (x+3)(x + 1) Select one: True O False - dx Then, by 2(x + 2) (x+3)²(x + 1)²

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: Differentiate y ' 1+ 1 ਕਲਿਜਲ z+Vi+va 1+

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Q: 4 find the difference quoitent of... f(x) = -√x-19

A: To find the difference quotient of the following function.fx=x-19

Q: 13) Use the product rule, quotient rule and/or chain rule to differentiate each of the following…

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Q: x+ 6x +7 f(x) = {-x + 3 5 if x < -1 if -1<x<3 if x 2 3 f(2) = %3D f(-1) = S(-7) = S(3) =

A: The given step function is f(x)=x2+6x+7if x&lt;-1-x+3if -1≤x&lt;35if x≥3

Q: ) Prove that sech¯¹(x) = In ( ¹+ √¹-x²) X

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Q: If y = (1+x)8 (x + 1)7 True False then dy dr

A: We can solve this as follows:

Q: JUX² +2x-8 dx Evaluate lx + 1Wx + 1)* + 9 = l(x + 1) + Vtx + 1}² – 9|]+c 9ln (+ 1)/(x + 1)² – 9 –…

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Q: • prove that y` = = for y= (of (1+x)) 1+x²

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Q: The solutions of cosh(2x) = 8sinhx - 5 are a) x = ln (4+ √17) and x = ln (1 + in (1 + √2) b) x = ln…

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Q: Dy + y Prove that is equivalent to 1 for x 0. 16x

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Q: For each statement, either prove that it is true or come up with a counter example N(ATA) = N(A) ● •…

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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: (ii) w* +1 – 8(@) TOEY 4 2.

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Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: hd the invense transformof eack of t FX) 6x-5 FCx)=

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: -5= =DS"S"?{(m-3)x²+³"(m - m x- ? y)'-4myx] dydx

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Q: O Deltarentiatk with respect () Singe (X+1) (x-)

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Q: 4) f(x²+2) lnx dx = a) (+x) Inx--x+c b) (+2x) inx--2x+c c) (x² + 2) lnx--2x+c d) None of the above

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Q: x2 dx is (ax2+4)(x2+9)

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Q: dx (1)(- 2e * )

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Q: If f(x) = x + 3 and g(x) = x – 3, (a) f(g(x)) : (b) g(f(x)) = (c) Thus g(x) is called an function of…

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

Q: Prove that In( +VI-X²³) = In ( ¹+ √1-x²) sech ¹(x) =

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Q: [ *(1 + 2') dt = 1 + 2°) dt 14 + C In(7) In(14) 14t+1 In(14) 7t+1 + C In(7) 7t In(7) 9t + C In(9) +…

A: Given:       ∫ 7t(1+2t)dt

Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

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Q: RECURSION RELATIONS: L Jp(x}] = ° Jp=1(x), d.r Jp-1(x) + Jp+1(x) =2J,(x). Jp-1(x) – Jp+1(1) =…

A: As per our company guidelines, we are supposed to solve only the first three subparts. Kindly re…

Q: Question 1 Determine which of the following functions are a bijection from the set of real numbers…

A: f(x) = x11 - 7x7 is not one-to-one, as           0 ≠ 71/4 but f(0) = f(71/4) = 0   Consequently,…

Q: Evaluate х3 (x* — 1)3 dx x*(x* – 1)ª + C (x* – 1)* + C 16 4x4 (x* – 1)4 (x4 – 1)4 + C 16 + C 4

A: The given integral is; Integration of x3(x4-1)3.

Q: The closed form of the recursively defined function T(n) = 2 T(n-1) +3^ T(0)=20 Can be written in…

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