find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

Q: Use a linear approximation (or differentials) to estimate the given number.   sqrt(100.8)

A: Given that

Q: On which derivative rule is integration by parts based?

A: Integration by parts is based on product rule of derivative. Mathematically, Product rule of…

Q: Find the derivative of the function. f (x) = cube root of ( 1+ tant )

A:

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: Use linear approximation to estimate ln(.99)

A:

Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

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

A:

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

A: Answer

Q: Find the most general anti-derivative or indefinite integral and check the answer by differentiation…

A:

Q: Find a curve through the point ( 1 , 5/6 ) whose length on the interval [ 1 , 2 ] is given by ∫ 1^2…

A: The length of the curve y=f(x) from x=a to x=b is L=∫ab1+dydx2dx Now , Length of a curve on the…

Q: Find the indefinite integral and check the result by differentiation.

A: To Find: ∫4x-csc2xdx

Q: Use differentials to estimate the value. estimate =  exact value =

A:

Q: Use logarithmic differentiation to find the derivative of y. Y= x cos x divided by the squre root…

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Q: Use logarithmic differentiation to find the derivative dy/dx if ( 3 square root of x )^y = (3 square…

A: Use logarithmic differentiation to find the derivative dy/dx if ( 3 square root of x )^y = (3 square…

Q: The second derivative of function: Inesina will be Select one: O sina O -sinz

A:

Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e". %3D Equation:

A: To find the equation of the tangent line to the graph of: y=f(x)=ln(-x) at x=x0=-e4 The equation of…

Q: Find the derivative y=arctan(square root 1+x/1-x)

A:

Q: Find the derivative using logarithmic differentiation if sin^-1 (2x). y = (tan x) where 0 < x < 1/2…

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Q: Find the derivative. Simplify where possible.

A:

Q: Find the anti-derivative: x2/3 dx. Upload Choose a File

A: Using simple integration method to solve the question.    Attached below is the detailed solution.

Q: An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A: We will estimate the volume of cylindrical metal as following. Inside radius = 2 cm Inside height =…

Q: Find anti-derivative if possible of: sqrt(tan(x))  dx

A:

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 f(x) = sinh (x) + 2 cosh (x) - sech (x)

A: Aim: We have to differentiate given function.

Q: Use logarithmic differentiation to find the derivative of the function. y = (sin 3x)In x sin()…

A: Formula used:If (x) and g(x) are two differentiable functions, then following rules  are efined as;

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

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

A: To write: Formulas for differentiation and integration.

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: The circumference of circle was measured to be 24 cm with possible error in measurement of 0.2 cm.…

A:

Q: Find the derivative of the function. y = 9 arcsin) – x/9 – x² Step 1 Rewrite the given function y =…

A: Given: --------------------------------------------------------------------------------------------…

Q: find integral sec 3 x dx

A:

Q: Use logarithmic differentiation to find the derivative of y. y= x cos x divided by the square root…

A: Consider the following equation: y=xcosxx+2 Take natural logarithms of both sides:…

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

A:

Q: Compute the derivative. Use logarithmic differentiation where appropriate. dx (6xj8x 8x dx (6x)

A:

Q: Find the derivative of y = arctan(x) by using implicit differentiation on x = tan(y).

A: Consider the provided function y=arctan(x).

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 cosh æ In(sinh x)dx.

A:

Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

A:

Q: Compute the derivative. Use logarithmic differentiation where appropriate. 10 1+ dx 10 1+ dx 10 In…

A: Answer: ddx1+10xx = ln1+10x-10x+10 1+10xx

Q: Find the derivative. Simplify where possible. y = x tanh-lx + In /1 – x²

A: We have to find

Q: Evaluate integral x^2e^-x^3 dx

A:

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

A:

Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

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: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: (21 -x' - 2x + 3)dx Vs 2 ds

A: We use power rule to find antiderivative .

Q: 2 cosh x+sinhx

A:

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. y = x tanh  -1 x +ln ( sqrt 1 - x 2 )

A: Given, y=xartanh⁡(x)+ln⁡(1−x2)can be rewritten asy=ln⁡(1−x2)2+xartanh⁡(x)