(b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

Q: 2. LOshx-Sin hx1 2. Co

A: We use hyperbolic Trigonometry identies

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A: sol)Given cos h 2x-sin h 2x=e2x

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A: Find your answer below

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A:

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A:

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

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A:

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Q: How can the graph of y = sin-1 x be obtained from the graph of the restricted sine function?

A: given: y=sin-1x

Q: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

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A:

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Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

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Q: sin( 2 cos (x/ 20 )) = Select one: O 2x (400 - x )°/(400 - 2x) O 40 x/ (400 + x) O ( 2x - 400 ) /…

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Q: Find ∫sin3 x cos4 x dx.

A:

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: 4 cos () dx 10. x³ sin3

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Q: If Z= sinh () x- show that:

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Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

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Q: 12 tan (4.x) sec (4x) dx S cos(11x) sin(2r) dx COS

A: Given that integration and we solve this integration by using general formulas of integration. Here…

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Q: 4 If cos x = csc x < 0, then sin 2x = cos 2x = tan 2x = ||

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Q: cos^2x+sin^2x/cos^2x=

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Q: Find sine half range for f(x) = \cos xl for -1<x<1 COSX for 7 < x < 0. f(x) for 0<x< 7. COSX

A:

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: 3 cos xdx 1-sinx

A:

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: do sin 0 – cos 0 cos 0

A: The given integral is ∫dθsinθ-cosθ

Q: 2. / sin² cos² xdx

A: As per our guideline we are supposed to answer only one question you can repost other in next…

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A:

Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

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Q: . Evaluate cos 3x sin² 3x dx

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Q: 8 sin(2x) cos(2x) dx

A: We have to evaluate the given integral

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

A: