38. A. -arcsin x x Vx2 – a² 39. 1 В. -arccos x a2 + x2 40. 1 С. | -arccot x Va? – x2 - D. -arccs x 1.

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Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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A: Differential equations

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A: y =a tan3θ   ,   x = a sec2θ     'y' is a function of 'θ' and 'x' is also      a function of…

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A: y=1212lnx+1x-1+arctanx⇒y=1212lnx+1-lnx-1+arctanx    ∵lnxy=lnx-lny⇒y=1212lnx+1-12lnx-1+arctanx

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A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: Evaluate 112x C: arc on y = x5/2 from (0, 0) to (4, 32) (2x - y) dx + (x + 3y) dy.

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Q: 1: A)find the length of the curve y=3(x)/2 – 1 from x=0 to x=1 ? B) Prove that: cosh (x + y) = coshx…

A: A) Length of the curve is y=3x32-1 B) Trigonometric function

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Q: 6.) y'of y = Insin(arctan 3x)

A: This is a basic differentiation question

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A: derivative

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A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

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A: Use the formula of coshz and sinhz in terms of exponents.

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Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

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Q: Q3: Find lim,- (2 – sin –) إجابتك :Q4 For (3x³ – 5x) V2x+1 find dy/dx at x=0 إجابتك

A: Explanation of the solution is given below...

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Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

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A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x3/2 from (0, 0) to (4, 8)

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Q: 5. Find de for y = 3csc x + x2 dy On= -3ese(#)cot(2) + 1) dy = -3csc x)cot ( x 10 dx O 2) dy…

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A: Solution is given below:

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

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