limit x to infinity (1+sin(3/x))^x

Q: .find integrals by using Beta fun dx (1-x*) ーズ

A: Using the Beta function, it can be written as follows.

Q: Find the indefinite integral.

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

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: Find the indefinite integral.

A: According to power rule of integration .

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

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Q: the

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Q: Limit as x approaches 0 1-cos(x)/sin(x)

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Q: 10) lim TT X-- sinx-cosx - TT X- 4

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Q: What do the limits lim h-->0 ((sin h)/h) and lim h-->0 ((cos h - 1)/h) have to do with the…

A: Show the expression for derivative of sinx0  as follows:

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

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Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

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

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

Q: If f(x) = x cosh x + 5 sinh x then f'(x) =

A: Find the derivative

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

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

Q: Find the indefinite integral ∫cosh2 (x − 1) sinh(x − 1) dx

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Q: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

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: Find indefinite integral.

A: Let the given integral be y - y = ∫x12+3x-23 dx      Identity to be used - ∫xndx = xn+1n+1+C

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: Find the indefinite integral ∫ (6 sec x tan x − 5 sec2 x) dx.

A: Given:  Let I=∫6 sec x tan x-5 sec2 xdx To Find: To evaluate the given integral.

Q: Problem x√x+1 dr

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Q: how do limits relate to derivatives and integrals? also give examples of when they are used to…

A: Limit of a function is defined as , Let I be an open interval containing x0∈ℝ. Let f : I→ℝ . Then…

Q: (b) Use the definition to show that cosh(-x) = cosh(x). + e-(-x) cosh(-x) e-X + eX

A: Please refer the attached image for complete solution. THANK YOU.

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

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

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

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Q: In(sin 4x) \ In(sin 8x) lim x → 0

A: We have to evaluate the limitlimx→0ln(sin4x)ln(sin8x)

Q: Find the indefinite integral ∫sec2 (x/2) tan (x/2) dx

A: Given: I=∫sec2x2tanx2dx

Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: Find all values 197. gh of aci on the the graph of f(x) = -3 sinxcosx where the tangent line is…

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Q: Find the indefinite integral for

A: The indefinite integral ∫-sinx+3cos-3xdx ∫(−sin(x)+3cos(3x))dx

Q: f(x) = ln(125 sin^2(x))

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Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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Q: Find the first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: Use the first derivative test to identify all relative extrema  f(x)= 1/2x-sinx on the interval…

A: Maxima or minima: If f(x) is any function: 1) Evaluate f'(x)=0 for critical point. 2) Evaluate…

Q: if X #0 メ=ロ Frnd continuous

A: given the function fx=xx if x≠00   if x=0 we know that x=x if x>0x=-x if x<0 therefore,…

Q: Find limit   without using derivative

A: Given,

Q: how do you express lim,,→ Li=1 Σ! as п 1+ definite integral

A: We know that

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

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Q: The L'Hopital rule and The derivative of the exponential function. lim (ex + x³)*:

A: Use l hospital rule

Q: Calculate the derivative. y = In (tanh (5x)) (Express numbers in exact form. Use symbolic notation…

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Q: Find the indefinite integral ∫ x2 sech2 x3 dx

A: We have to find indefinite intrgral  ∫x2sech2x3dx We have ∫x2sech2x3dx  Take x3=t⇒3x2dx=dt⇒x2dx=13dt…

Q: Compute limx→0 sin(x) − x divided by  x^3

A: We have to evaluate the limit: limx→0sinx-xx3 After putting limit value we can see that this is 00…

Q: 3-sinx 6. f(x) = 1+ In(x3 — х)

A: Quotient rule of differentiation: Chain rule:   also

Q: Find all points on the graph of the function f(x) =2 Sin x + Sin2 xat which the tangent line…

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Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

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Q: Find lim Sin 3x (1- Cosx) メーや。 メ*s X Sinzx cosx

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Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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