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Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

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Q: Integrate sin^2(7x)-cos(x)

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Q: sec 3x tan² 3x dx

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Q: Find the indefinite integral.

A: We have to solve the indefinite integral: ∫tan x3 sec2 x dx Solving the integral by substitution…

Q: EX / Show that cosh x-sinhx=1

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Q: find f'(x) if f(x) = tanh(ln x) +sin2(2x)

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Q: Find the indefinite integral ∫sec5 x tan3 x dx

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Q: Express in exact form: In(x² + 1)dx

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Q: find the derivative.

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Q: Find the differential of z = sin²(5x) + ev

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Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

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Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

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Q: 5. COS 5. - cos vx dx x1

A: Indefinate integration problem.....

Q: 2. Evaluate the integral: | sinh x cosh² x dx

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Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Find the indefinite integral. ∫(sec 2x + tan 2x) dx

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Q: Find the derivative of O 2sec 2x 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

A: I have stated the used formulas in the solution

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: Evaluate the indefinite integral: ∫ sec2 x tan4 x dx

A: Evaluate the indefinite integral. ∫sec2xtan4xdx Let tanx=tsec2xdx=dt

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: Find the indefinite integral ∫sec6 4x tan 4x dx

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

A: see my solution

Q: Find the indefinite integral ∫tan3 x/2 sec2 x/2 dx

A: we have to find the value of indefinite integral  ∫tan3x2sec2x2dx let the given indefinite integral…

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: find integral sin 5 x  cos 2  x dx

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Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

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Q: Find the indefinite integral

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Q: */16 etan(1r) sec2(4x) dr

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Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: Evaluate the integral. sin (12x) cos (7x)dx | sin (12x) cos (7x)dx =

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Q: Find the derivative of y(x) = In (8(In(x))'). (Use symbolic notation and fractions where needed.) dy…

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Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: Use the hyperbolic identity cosh(2x)= 2 cosh2 (x)-1 to solve 4 cosh(2x)– 22 cosh(x)+ 19 = 0 .

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Q: Use differentials to estimate sin (π/6 + 0.01).

A: Use differentials to approximate the value of sinπ6+0.01 The nearest number to sinπ6+0.01 whose sine…

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Find the indefinite integral and check the result by differentiation                   ∫(x2 −…

A: Given, I=∫x2-932x dx

Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: Evaluate the indefinite integral.

A: It is required to evaluate the indefinite integral:

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: Left in implicit form

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Q: Verify the differentiation formula.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.