Evaluate using trigonometric substitutio dt | (912 + 4)2 *

Q: Find Taylor's Sen'ed fey ci) f(x) = sin (2) about x= 1

A: see 2nd step.

Q: sin(x) + 1+x20 dr

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Q: Prove the following  (sinx)(secx)(cotx)= 1

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Q: Assuming Cov(X, u) = 0 allows us to equate Exû to zero. True or False? Explain.

A: Solution

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2 x = 1.

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Q: What would you substitute the integrand with in order to evaluate cos(29x) cos(31x) dx? (Do not…

A: The detailed solution is as follows below:

Q: prove that tanx V secrsinxtanx

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Q: find maclurin formula in the fourth degree for f(x)=secx

A: To write the maclurin formula in the fourth degree

Q: Evaluate the integral  ∫(7(1-tan^2(x)/sec^2(x)) dx

A: We have to evaluate ∫71-tan2(x)sec2(x) dx

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: Comvert to retangular coodinates. Use exct values.

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Q: V/ Prove that: (1) tanx= cot

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Q: esirq) . cos(q) dq 5x/2

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Q: Evaluate fi' sin(21*)dt

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Q: If Y=tanx prove that %3D2

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Q: Evaluate using cauchy's Residue Evaliate theorem.

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Q: Evaluate the integral f sin²x cos³xdx.

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Q: Evaluate the definite integral. | (ci + Vij + 6tk) dt

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Q: What is the integrable form of sin-cos- sin0 do?

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: sin 3) Prove licen

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Q: In (a le) secx ((2- sec²x) " sec (3А - x) to be integrable using the formula What should be the…

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Q: Evaluate the itegral by interpreting it in terms of areas. 0. 3 + 100 - x2 ) dx -10

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Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2x = 1.

A: To show that cosh2x - sinh2x =1.

Q: 8. Use Trigonometric Substitution to evaluate x'V4+x?

A: We will use standard formulae of trigonometry.

Q: Prove the following identitv Show at least 4 steps in working out. sin x-cos x sin x+cos x sec x csc…

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Q: Q4: Prove that: secx • cscx = tan x + cot x

A: According to guidelines we should have been able to solve only one question at a time #4

Q: Prove (05t - sin 4t tos?t

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Q: HW/ Prove that: (1) 1-tanif x sechx

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Q: evaluate using the appropriate method or combination of methods.

A: We will need by parts method with

Q: @H-w/ prove that cosiz=coshz

A: We have to prove by using cosiz and coshz formulae.

Q: Find Maclaurin expression of f(x) = Cosh (x)

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Q: Prove the following 1/tanx+cotx=sinxcosx

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Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

Q: Prove that the inequality sinx+tanx>2x holds in the interval (0,π2).

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Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: Evaluate the integral ∫tan7 x/2 sec2 x/2 dx

A: We have to evaluate the integral: ∫tan7 x2 sec2 x2 dx Here we will use substitution method since…

Q: Determine the exact function value of cosh (In 2).

A: The given function is  Cosh(ln2)

Q: © Find the singular value deomposition of the matix I- A =

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Q: What is the integrable form of sin-cos-sino do?

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Q: 3) Prove that b) tan- (*)} = sechx

A: Evaluate the derivative of the given function as follows. ddxtan-1ex=11+ex2ddxex…

Q: Prove using the INT. tan- 1 x = cos- 1 x has a solution.

A: Given:         tan-1x=cos-1x Solve:       tan-1x=cos-1x  ⇒x=costan-1x      ................1

Q: EVALUATE 3 TT e Sinxcosxdx USING SIMPSON RULE 20 土

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Q: prove that tanx V secxsinxtanx

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Q: Prove the following identity (Sin x - cos x)^2 = 1 - sin(2x)  show work

A: Given: sinx-cosx2=1-2sin2x

Q: compute:   ∫sin^3xcos^2xdx

A: We have to find:

Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

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Q: B.Determine the values of n and h required to cprovimate sin3xdx to within 0.0002. Use Composite…

A: Error in calculating the integral I=∫abf(x) dx by using composite Simpson's rule is given by…

Q: Prove that _ d tanx = Sec'x.

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Q: 3-Expand In [x? sin³ x /vx2 +1]

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Q: Define Rolle's Theorem. With the help of Mathematica, show the applicability of the theorem en…

A: Rolle's Theorem: Let a < b If f be a continuous function on the closed interval [a, b]  and…