8. Differentiate the function (use long method): y = Va² + x² .

Q: Integrate the following function by using trapezoidal rule. 142*dx

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Q: Using the Constant Multiple Rule InExercises 25–30, complete the table to find thederivative of the…

A: The given function is, y=5x2-34. The objective is to find the derivative of the function by using…

Q: Use the sign of the derivative to establish the inequaltiy In(1+x) > I -,V> 0. 2

A: See the attachment

Q: ind y' by implicit differentiation: xy3 - sqrt (x2 +1)=2y

A: Definition used -    Implicit differentiation-  If equations do not define explicitly y as a…

Q: By using first principle of differentiation find f'(y), if ƒ(y) = Му—N

A: Given: f(y)= My-N According to the first principle of differentiation, the derivative of a function…

Q: 10. t(x) = Vx+3+4

A: Given function t(x)=x+3+4

Q: Differentiate f (x) = vx from first principles. %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Differentiate the function.   y = x + 1/ex

A: Case (I): If we have the given function as y=x+1ex        ⋯⋯1 We know that, from the quotient rule…

Q: Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

A: Given:        ∫02x2+1dx       n=4 , a=0, b=2   Midpoint Rule…

Q: Use a linear approximation to estimate v100.5. Show your work.

A:

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: The firm is very interested in maximizing profits. Its profit model is given by the function: f(x) =…

A: Solution is given below:

Q: What function should be used to minimize the distance between, y = 3x2, and the point (0, 2)?

A: y=3x2,  0, 2.

Q: general

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Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

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Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: Differentiate: F(y) (y + 9y°) yA - y?

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Q: Find the length of the curve y=lnx from x=1.5 to x=3.

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Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: Find the relative extrema of f(x) = 8+72x – 9x? using both first and second derivative tests. f (x)…

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Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: y =

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Q: • Use the trapezoidal rule with n = 14 to estimate: -dx √√1+x²

A:

Q: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: Find the derivative of the funciton F(x) = dt. F'(x) =

A:

Q: find x which minimizes the following function and its minimum with differentiation technique.…

A: We will find out the required solution.

Q: Find the antiderivative of x/sqrt (x2+1) and verify it by differentiation?

A:

Q: How is the antiderivative of a function related to the function?

A: Given: antiderivative of a function related to the function.

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Differentiate the function. y = In(eX + xe )

A: In this question first apply the property of log and then differentiate as shown...

Q: Does Newton’s Method fail when the initial guess is a relative maximum of f ? Explain.

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Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. (3.97) =

A:

Q: 8. use the method variation o f parameters to find the general SOlution ot y"+ y =secX

A: G ji

Q: What is the maximum slope of a tangent to the function f(x) = −x3 + 4x − 2?

A: Maximum slopes of tangent to function is 4.

Q: Find the critical point of the function. Then use the Second Derivative Test to determine whether it…

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Q: Explain graphically: The endpoint approximations are less accurate when f , (x) is large.

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Q: Find the point P on the line y=3x that is closest to the point (40,0). What is the least distance…

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Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Find y ' by implicit differentiation for 4x² y7 – 2x = x5 + 4y3 . %3D

A: We have to find y' by implicit differentiation of : 4x2y7 - 2x = x5 + 4y3

Q: Use the variation of parameters method to solve y" + y = secx.

A: A differential equation is given. We need to solve it by variation of parameters.

Q: Use a linear approximation to estimate V8.05.² Show relevant work to explain your reasoning.

A: Linearization: If y = f(x) is differentiable function at x = a, then linear approximation at the…

Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

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Q: y 1-

A: The solution is given below in the next step:

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

A: