let f(x) = 2x^2+2x+3 and let q(h) = f(1+h) - f(1)/ h.    Then q(0.02) = ?

Q: Find the general solution using Reduction of Order: y''=2lnx

A: Explanation of the answer is as follows

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Analyze the critical points of f (x) = (2x − x2)ex .

A: fx=2x-x2ex Differentiating with respect to x, we get…

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x³ + 15x² + 24x – 3

A: We Know that The second derivative may be used to determine local extrema of a function under…

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: Find (f - g)(x) if f(2) = 7x³ – 52² + 42x – 30 and g(z) = 7 O (f · g)(x) = 49zª + 269x² + 150 O (f·…

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Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

A:

Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: Use the first derivative test to locate all local extrema for 3 f (x) = -x'+ = -x' +- x +18x.

A: Explanation of the answer is as follows

Q: 2 - ) at x = 4 1+ x)

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Q: Find the area of a triangle bounded by the yy axis, the line f(x)=4−67xf(x)=4-67x, and the line…

A:

Q: In terms of limits, what does it mean for ƒ to grow faster than g as x→ ∞?

A: Suppose we need to find out limits  And f(x) grows faster than g(x), Then denominator gets much…

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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Q: x³tanh² (x*) sech²(x*) dx

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Q: Find f(-3). -2 -4 www.analyzemath.com 1 O 2 Оз -1

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

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Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: 15. Differentiate using quotient rule: x+2 y = х-2

A: Given, y=(x+2)/(x-2) Then,dy/dx will be

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=3−16xf(x)=3-16x, and the line…

A: GIVEN DATA: Triangle is bounded by the equation of line fx=3-16x                         line…

Q: Find all the critical numbers for the function g(x) = % xª -- x3 - 5x?

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Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

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Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

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Q: Find the derivative of the function by the limit process. f(x) = x3 − 12x

A:

Q: Find the root between [-1,0] where f (x) = (x+2)' +2x – 5 with error epsilon=0.1 by using False…

A: There are many methods to find the roots of an equation in a given interval. One among such method…

Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

A:

Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given,          The function is fx=7x-9.

Q: Fexiy)= 2+3トなら-3A Ris Rectanghe ( (ろy)と1メ,-

A: This is a problem of maxima and minima. By using first derivative test we will find out critical…

Q: Locate and classify all the critical points of the function.(If an answer does not ex g(x, y) = 4x2…

A:

Q: Find the derivative by the limit process. f(x) = 11-x²

A:

Q: Find the extreme values of on [-2,2]. f(x) = ret, x < 0 2x³9x² - 12x, x ≥ 0

A: Solution of given question is written in below steps.

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

A:

Q: The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1…

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Q: f (x) %3D х3 -Зх2- 2 3x2

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Q: Solves methad of vriation of Parameters - secx by the yot gosx +イne

A: We use the method of variation of parameters to solve this problem.

Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: 4. Find derivatice y 4=In (x 3-4x²+1)

A:

Q: Find the critical points of the function f(x)=x2lnx.

A: We need to find the critical points of the given function.

Q: If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f…

A:

Q: The critical points for the 4 function f(x) = x + – is:

A: Given,          The function is fx=x+4x .

Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: The coordinates of the critical point according to the criterion of the first derivative of the…

A:

Q: Find the derivative by the limit process. F(x) = 13 -

A:

Q: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…

Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

A: