For what values is the function f(x)= ln(x+1)/x^2+1 continous? Can you please explain how to approach this problem.

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: 1+ln(3x²) y = 1+ln(4x) ||

A: Given function - y = 1+ln3x21+ln4xDifferentiating on both sides with respect to x - dydx =…

Q: Suppose we want to use logarithmic differentiation to calculate the derivative of y=x²x . As a first…

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Q: Find the derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: Give 1 problem for differentiation rule of exponential

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Q: fx ln x dx.

A: According to the guidelines the first question can be solve in multiple question. Kindly repost…

Q: 2. f(x) = 3. g(x) = 5 In x – 2* 4. g(x) = 4x³ log, x

A: To find the derivative of the given function. 2). Given function is fx=x2ex. Quotient rule of…

Q: 1. у %3D х+/x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: kel derivative

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Q: Find the derivative of ƒ (x) = 8ª ln (x).

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Q: What are the formulas for differentiation and integration?

A: Differentiation formula: There are many formula available in differentiation. few of them listed…

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

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: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: 5th derivative of y = log x^5 to the base 2

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Q: Write the equation of the tangent and normal lines to f(x) at x – 1 x = = 4.

A: Consider the given function fx=x+1x-1 at x = 4. Tangent line: Obtain the y-coordinate of the point…

Q: Find the derivative. Simplify where possible. f(x) =ln  ( cosh x )

A: fx=lncoshx

Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: y у %3 4a/сosh a

A: Consider the given hyperbolic function y=4acosha The given function can be written as, y=4acosha=4a…

Q: find derivative y=square root of (1+ x times e^-2x)

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Q: what is the differentiate of f(x)=ln x

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Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: Differentiate the following function.   y = ln(3x+1) - ln 3

A: We need to differentiate the following function.   y = ln(3x+1) - ln 3

Q: State the derivative rule for the logarithmic function ƒ(x) = logb x.How does it differ from the…

A: Given: fx=logbx for finding derivative of given function, first we convert it's base in e then…

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

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Q: What are the formulas for differentiation and integration? How are they applied?

A: To write: Formulas for differentiation and integration.

Q: What are the domain and range of ln x?

A: Given: y=lnx we know that in lnx, x>0 so, domain of given function is x>0

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: What is the first derivative of q(x)=(3x)7x at x=2?  Enter an exact answer in terms of a natural…

A: When there is variables in exponent we should take log both side then differentiate. Here we use…

Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: Derermine The FirST derivative of : 千irsT OF F) = x³ .16 V5メ-2 こSioN Expa usiNG Logalith mic Ex…

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Q: 2. y=cot1-2x 3. y=log22x*

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Q: What are the formulas for differentiation and integration? How to apply those formulas?

A: See the attachment

Q: x(2x+3) 17. f(x) =- (x° +1)

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Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

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: How is ln x affected if x is multiplied by et?

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Q: What is the derivative of: log x/(x+1)

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Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

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Q: Find the second derivative of 2x^2 ln (1/x^2)

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Q: 1. Find the derivative of f(x). 3x3 – 2x2- x- 5 | (a) f(x) =

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Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

Q: Find the derivative using logarithmic differentiation. x(x + 4) (5x + 1)(3x +7) (Express numbers in…

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Q: Find the derivative of the function. y=arctan(sqrt 1-x/1+x) Also, Would I be able to use…

A: Given :  y = arctan1-x1+x

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: Find the derivative. Simplify where possible. g(x) =   cosh (   ln x )

A: Given: gx=coshlnx

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: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10