ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

Q: Express the limit as a definite integral on the giveninterval.

A:

Q: Evaluate the definite integral.

A: We have to evaluate the integration ∫0π3sec32xtanxdx

Q: 7. S(2 + tanx)²dx

A:

Q: Find the indefinite integral.

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

Q: Evaluate the definite integral S (1+ 2x) dx using Riemann sum.

A:

Q: Evaluate the integral. ∫0 π/3 tan5 x Sec4 x dx

A:

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = θ + sin2 (θ/3) - 8, (-∞,…

A:

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

A:

Q: 3 dx by Simpson's rule breaking it into 6 intervals. Evaluate 2+x?

A: We have to evaluate the integral ∫2532+x2dx by Simpson's rule-breaking it into 6 intervals.

Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

A:

Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

A:

Q: Evaluate the indefinite integral: ∫ sec θ tan θ(sec θ − 1) dθ

A: Given: ∫secθ tanθ (secθ-1) dθ

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(æ')…

A:

Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

A:

Q: Find the indefinite integral ∫ 3√(tan x) sec2 x dx

A: ∫tanx3sec2x dx Now put tanx=t⇒sec2x=dtdx⇒sec2x  dx=dt

Q: 23. Find the point c that satisfies the mean value theorem for integrals on the interval [1,4] for…

A: The given function is: f(X)=2x2-7x, [1,4]

Q: Evaluate the indefinite integral: ∫sec x tan x dx

A: Given indefinite integral is ∫secxtanxdx

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

A:

Q: he average speed / (t) (measured in kph) of traffic in a certain PM to 8 PM on a typical weekday is…

A: Given:

Q: Show that O tanh(In x) = x² -1 O (cosh x + sinh x)" = cosh nx + sinh nx %3D

A: From the given problem:   tanhlnx=x2-1x2+1   As we know that :   sinhx=ex-e-x2 ; coshx=ex+e-x2   So,…

Q: None Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

A:

Q: Evaluate the indefinite integral.

A: Consider the given integral I=∫sec3x·tanx dx

Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

A:

Q: ) Use Taylor's formula to estimate the error in the approximation In(x) ~ P3(x) or all x in the…

A: Since you have posted multiple questions but according to guidelines we will solve the first…

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

A:

Q: Use a tangent line approximation to estimate the value of V3.9 O 2 O 1.998 O 1.975 O 1.95

A: Known fact: The tangent line approximation formula is fx+∆x≈fx+f'x ∆x. Given that 3.9. Consider the…

Q: Show that O tanh(In x) = (cosh x + sinh x)" = cosh nx +sinh nx

A:

Q: Use Secant method to find the root ofthe function:f(x) = 3x + sin x- e to 5 decimal places. Work…

A:

Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

A:

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

A:

Q: Example. Sind Susface area of Z- S4-X2 above ২-

A: Recall:  Surface area, A=∫∫R1+zx2+zy2dA We have, z=4-x2,  R=[0,1][0,4]

Q: rmine whether sin z is convergent.

A:

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(x)…

A:

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: Find the indefinite integral (2 sec x tan x +9 sec? x) dx. |(2 sec x tan x +9 sec? x) dx =

A: Integration appling rule constent cofficenat.

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = 3 tan θ - cotθ - θ, (0,…

A: Show that the functions have exactly one zero in the given interval. r(θ) = 3 tan θ - cotθ - θ, (0,…

Q: evaluate the improper integral / 1 dx. Does it converge x(In x)2 diverge? Justify your claim.

A:

Q: In n n=2

A: The given expression is, ∑n=2∞lnnn The integral test says that for a series ∑n=2∞lnnn converges if,…

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

A:

Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: 8. Use Simpson's rule, with n = 8, to approximate fe sint dt. Compute the error if the true value

A:

Q: 1. cosh (j) 2. tanh 3. 3. In(2 + j3)

A:

Q: Express the limit as a definite integral on the given interval. lim 2 x;)?+9 -ах, [1,4] (x;")² + 9'…

A: Use;∫abf(x) dx =limn→∞ ∑n=1n f(xi) ∆x                       over the given interval [a, b].

Q: Evaluate the definite integral S (1 + 2x) dx using Riemann sum.

A:

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A: