Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h0 f(x) = x³ %|

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A: a. ∫4sinx+7cosxdx=4-cosx+7sinx=-4cosx+7sinx

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Q: (a) Determine whether the Mean Value Theorem applies to the following functions on the given interva...

A: Hello learner, we can solve all parts of first question as per the honor policy. Please resubmit the...

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A: Given

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A: (x-h)2=4p(y-k) , Vertical parabola.Vertex - (h,k)Focus - (h,k+p)

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Q: у %3D Зx5 — 15x4 + 20х3 + 3 -

A: Given : y=3x5-15x4+20x3+3   To Find : x & y- intercept of the given graph

Q: Within the interval ( -0.92, 1.69 ), for what value of x does f(x) take on a minimum if f(x) = -3 si...

A: Let's find. 

Q: GIVEN: Center (-4,3) and P (1,-1) CIRCLE Find the Standard Form and the General Form

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

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A: Given that fx=-3-x23Solution :if f'x  +ve to -ve then maxima occurs .if f'x  -ve to +ve then minima ...

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A: This question can be solved using future value of ordinary annuity for the first 8 years and then ap...

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Q: b. Recall that f(x) = 2*-1-1. Graph of fi(x) = f(-x) + 2, f2(x) = f(-x+1) + 1, and fs(x) = f,(x) + f...

A: The given function,          fx=2x-1-1

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A:    We have to apply properties of polynomial to find the correct graphs. 

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A: Topic:- application of integration

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Q: Determine the graph of the second degree equation x? + y² – 6y + 2x + 10 = 0. NONE OF THESE Imaginar...

A: We have to choose option

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Q: Find the area of a triangle with the given description. (Round your answer to one decimal place.) a ...

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Q: Question 9 5x2 tan( 3x) dr. ifu=3x*, then the resulting integral is SFlu) du. Find Given: A 18 none ...

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Q: Determine whether the series converges. k=1

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Q: Within the interval ( -0.92, 1.69 ), for what value of x does f(x) take on a maximum if f(x) = -3 si...

A: solution:-f(x)=-3sin(2.4x)+3.9cos(2.4x),     x∈-0.92, 1.69f'(x)=-32.4cos2.4x-3.92.4sin2.4xfirst deri...

Q: Find the orthogonal trajectories of the family of curves y = kx'. = C (C) 3 y³ +x? = C (D) 3 y³ + 3 ...

A: Orthogonal trajectory

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Q: Question 1 dx The integral can be re-written as A lim (-1+2 y 1-m m - 0 B none of the choices lim (2...

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Q: Identify the parent function and the transformation shown in the graph. Write an equation for the fu...

A: Given : A graph that has following coordinates  (x, y) --> (0, 2) , (4, 0), etc When x= 0,y=2 tha...

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Q: cot (2x) -dx. Evaluate the integral V cot2 (2x)- 15 csc (2x) CSC A --Arcsec 8 +C 4

A: I=∫ cot(2x)cot2(2x)-15I =-∫ -cot(2x)csc(2x)csc(2x)csc2(2x)-1-15 dxcsc(2x)=u-2 cot(2x)csc(2x) dx = du...

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A: topic- logarithmic equations

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Q: Use the binomial series to find the Maclaurin series for the function. 4 f(x) = V1 + x 1 f(x) = 1 +-...

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Q: 1. Evaluate the limit if it exists. If it does not exist, justify. 2 cos(3x? + 5) + [6x² +2] (a) lim...

A: Please see the below picture for detailed solution. 

Q: f(x) =(x^2/3 − 1)^2 -Take note that the 2/3 is the exponent of x -please answer sub part c,d,and e...

A: According to question,Given Function,fx= x23 -12

Q: Use the difference a,41 - a, toshow that the given sequence (a, ] is strictly increasing or strictly...

A: We can solve the following problem as:- Here N= {1,2,3,.......n...}