Use the four-step definition of the derivative to find f'(z) if f(x) = 91²-31 - 20. You may have to simplify your answers to recieve credit. f(x + h) = f(a+h)-f(x) = f(a+h)-f(x) h f'(x)= =

Q: 2. Let g(x) = arctan(x²) — ln(1 + x¹). Find the equation of the line tangent to y = g(x) at x = 1.…

A: Given:- gx=arctanx2-ln1+x4

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A: To Find : Computation it models through given figure

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A: To find the critical points for given function

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A: Solution: By using exponential regression graph plotter

Q: Det

A: Both the series will converges....for detail go through the solution

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Q: 2. A population y grows according to the equation dy the population doubles every 21 years, then…

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Q: me: 3. What does the lim h 0 f(x+h)-f(x) h Date: 2 =- - 4 indicate about the graph of the function…

A:

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A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: d the distance from the point (5,9,-6) to the plane - 3z = amon 18.

A: we will find the required.

Q: 1. Find the indicated limit or state that it does not exist. (1) lim (x²y+3x) (2) sin(x+y) lim…

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Q: Let the function f(x) have the property that f'(x) g'(x) = = = x+5 x-2 ¸ If g(x) = f(x²) find g'(x).

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Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

A:

Q: Find a plane through the points (-5,-6,2), (2,5,7), (-6,-4,6)

A:

Q: At what points is the following function continuous? 6x tan x x² + 3 y= Choose the correct answer…

A: Given function:- y=6xtanxx2+3

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Q: A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the…

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Q: Find the radius of convergence of the following power series: summation from n = 0 to infinity…

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Q: Itranscript a. Determine whether the Mean Value Theorem applies to the function f(x) = In 16x on the…

A:

Q: Find the distance between the skew lines r(t) = (5, 0, – 3)t + (− 8, 7, - 2) and p(s) =(2, 1, 4)s +…

A: I have done solution step by step in detail...go through the solution

Q: Solve the given differential equation. 7ydx - 7xdy+x+dx=3dx The solution is 0. (Type an equation.)

A:

Q: Differentiate y' = with respect to t. y = d cos(t) + t² sin(t)

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Q: The so-called cuspidal cubic is given parametrically by the equations x = t³, y = t² Compute the arc…

A: It is given that x=t3y=t2

Q: Simplify the expression Show your work 2 T 6x3-17x2+20x-5 3x1 PENCIL THIN BLACK B

A:

Q: Find the limit. lim (3x)² = (Type +0<x (Type an exact answer.)

A:

Q: Convert f(x) = 2x² + 5x-1 to vertex form O f(x) = 2(x + 5)² - 41 ○ f(x) = 2(x + ²)² - 33 8 O O f(x)…

A:

Q: 5. Consider a unit vector u = (a,b). (a) How many unit vectors are orthogonal to u? (b) Explain a…

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Q: 78. 1 2 4x + 12 2 (x² + 6x + 1) dx

A: Ans = 9/68 For detail ...go through the solution I have solved step by step in detail

Q: A ball is thrown upward. Its height hin feet is given by h(t) = 104t - 16t², where t is the time…

A: Given height:- ht=104t-16t2

Q: f(-1)=0 and g(-1)=-1  a. (f+g)(-1), b. (f-g)(-1), c. (fg)(-1), d. (f/g)(-1)

A: Given query is to find indicated function operations.

Q: lim X-70 3√√x+1-1 X

A:

Q: If position is given by p(t) = -1² + 5t, what is the velocity v(t) at t=2? ov(2) = 2 ov(2) = -1…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Suppose that f(5) = 1, f '(5) = 4, g(5) = -5, and g'(5) = 9. Find the following values. (a) (fg)'(5)…

A: Given query is to find indicated derivative.

Q: PTT/5 sin¹ (5x) dx =

A:

Q: Among all the points on the graph of z=7-x² - y² that lie above the plane x + 5y + 7z=0, find the…

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Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s as a…

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Q: If interest in a bank account is compounded continuously, the amount grows at a rate that is…

A: Solution: Given data, Initial amount P = $1000 rate r= 5% = 0.05 According to continuously…

Q: .) Find the volume of the solid whose base is the region bounded between the curve y=secx and the…

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Q: Find equations of the tangent lines to the curve x-1 x + 1 that are parallel to the line x - 2y = 3.…

A: Given  curve equation:- y=x-1x+1

Q: Is this fully simplifed ?

A: Find y' for the function y=6x-3x2+7x.

Q: 1. An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find all values of z at which the graph of f(x) = 2³² +42² +7 has a point of inflection.

A:

Q: Find the volume of the solid enclosed by the paraboloids z = 16(x2 + y2) and z = 2 - 16(x2 + y2)

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Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…

A: Given: Mx,y,z=12x-y2+xz+240The radius of the spherical planet is 12 unit. Hence, x2 + y2 + z2 =…

Q: The average rate of change of f(x) = ax³ + bx² + cx+d over the interval -1 ≤x≤0 is Oa+b+c 2d a-b+c

A:

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: g(u,v)=u2e-vpoint is (8,0)v=3i+4jDvg(u,v)=∇g(u,v).a→

Q: Is it possible to answer this using factoring, conjugate or any alternative methods? If so, could…

A: To evaluate the following limit. limx→0 x+13-1x