Find the length of the graph of y = (1/2) cosh 2x from x = 0 to x = ln sqrt(5).

Q: Find the indefinite integral sec* 7x dx.

A: To find the indefinite integral of ∫sec47xdx

Q: Sketch a graph of y = 8 on [- 5, 4] and use geometry to find the exact value of int -5 ^ 4 8 dx.

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Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: B- Find dy / dx for the following functions: (3 mark) * 1- Y= sin( coshx log, 2 )

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Q: Use implicit differentiation to find dy given y³2 – log(x²y¹) = cos¯¹(1). dx

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Q: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: find the length of the curve y = arcsin e^(-x) from x = 0 to x = ln 5/4

A: Given curve, f(x)=arcsin e-x from x=0 to x=ln54

Q: Find dx * for y = (x² + 2)°(1 – x³)* using logarithmic differentiation.

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Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Without using a graphing calculator, how can I show the function 1-ln(y )= z in a graph and its…

A: Without using a graphing calculator,  Show the function zx,y=1-lny in the graph and its traces.

Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

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Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

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Q: B- Find dy / dx for the following functions: (3 mark) * 1- Y= sin( coshx log, 2 ) 1 Add file 2- (3…

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Q: of the tangent line to the sine function at the origin. y y= sin(7 x) values with the number of…

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Q: Find the equation of the line tangent to xe^1−x at x = 1 and x/e * ln x at x=e.

A: To determine the tangent lines to the curve using derivatives

Q: Find the length of the curve y = ln(sec(x)), where 0 is less than or equal to x which is less than…

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Q: Find dy/dx by implicit differentiation. 5 5 y3 dy/dx = (Express your answer using positive exponents…

A: We have given 5/x^3 + 5/y^3 = 1

Q: Find dy/dx by implicit differentiation  sqrt(xy)=x2y+10

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Q: find the derivative of y with respect to the givenindependent variable. y = log2 r . log4r

A: Recall the properties of logarithms:

Q: sinh(3x) g(x) 3

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Q: 2. y = [log(arccotx³)]coshx. Find dy/dx

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Q: Find the indefinite integral ∫sinh 6x dx

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Q: (log a) dx 1+x²

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Q: Find dy/dx by implicit differentiation. 2 arcsin(xy) 3 arctan(4x), G 2) dy dx Find the slope of the…

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Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

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Q: dy for y =loge(l-Sin( 3x) Xア

A: We use chain rule to solve this differentiation

Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: The derivative of the function y = cos(x In 3) log3(sin x) is:

A: Given,            y=cosxln3log3sinxTo find : The derivative of the given function.

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: find dy/dx by implicit differentiation sqrt(xy)=10x+4y^2

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Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: Find the value of the definite integral: 4x dx -2

A: ∫-254x3 dx

Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: find the derivative of y with respect to the givenindependent variable. y = log3 r.log9r

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Q: The slope of the tangent line to the graph of y = ln x at x = a E R approaches infinity as a → 0+.

A: Given curve: y=ln x

Q: Find the surface area of a sphere of radius 5 by rotating the graph OI the function x2 between x =…

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Q: obtain the ava dient to Cu gra equation givey by メ= ln and sigh '2t wh 3.

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Q: Q2): If sinh(x) =find tanh(4x). %3D

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Q: Find the equation of the tangent line to the function f (x) = e*²-1 ln(x + 1) when x= 0.

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Q: a. Find the root mean square value of tanh x, for 0 < x< 2.

A: we know the formula of root mean square, rms = [ (1/b-a) (integration of |f(x)|2 from a to b) ](1/2)…

Q: With n > 0, does x" dx get larger or smaller as n increases? Explain graphically.

A: Given: The given integral is ∫01xndx. Calculation: Use the integral formula, ∫xndx=xn+1n+1+C.…

Q: Solve the definite integral e(arcsin(x)) dx. /1 – x²

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Q: sinh(cot(x)) x2 + 1 dx

A: To Determine: find the integration Given: we have ∫sinhcot-1xx2+1dx Explanation: we have an integral…

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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Q: Find the indefinite integral. sinh(2 – 9x) dx

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Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.