Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast and easy way? What is the final answer to this problem?

Q: 2. Use the Limit Comparison Test to determine whether the following series converge or diverge: a)…

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Q: Find the absolute minimum value of f(x) = 9x² - 5 x + 14 on the interval [0, ∞). Note: You need to…

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Q: Find the equation of the tangent line to the graph of the function f(2)=√1026 +26 at the point…

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Q: the Factor Theorem to determine whether x+2 is a factor of P(x) = 2x² + 3x² +4. cifically, evaluate…

A: Here given that x+2 is factor of p(x)  so according to factor theorem x+2 is the factor of p(x) then…

Q: Find the derivative of f (y) = 9 tan (y) V 2 12 y³√√

A: To find the derivative of the below expression. fy=9tany−y2−12y3y

Q: 1 3. How many terms of the convergent p-series k=1² must be summed to obtain an approximation that…

A: We have to find no. of terms of the convergent p series.

Q: 2e³y - ²x + 2y - 4

A: We will find the critical points.

Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate

Q: Question 2 a. I b. | function f(x, y) = y² − x² + — a 1 Find the critical points of the function…

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Q: Find a particular solution to the differential equation Ур || y" + 5y' + 6y=-108t³.

A: Given differential equation is y''+5y'+6y=-108t3 We have to find a particular solution for it.

Q: The equation implicitly defines as a function of t. Find dr dt da dt 11 2 cos (6 x) = -8

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Q: Integral Calculus (

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Q: Sketch the graph of the equation by point plotting. y = 5-x² -3 X y -2 0 2 3

A: Sketch the graph of the equation by point plotting

Q: Air traffic controllers continuously monitor the angles of elevation and to an airplane from the…

A: Concept: The angle of elevation: The angle of elevation is the angle created between the line of…

Q: ขน lim (x,y) → (0,0) x² +10y²

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Q: Consider the following function: f (x) = -1/2 x^4 +16x^2 -4 Determine f′(x) and f′′(x).…

A: Solve the following

Q: dy dx 2xy + 6x + (x²-4)-

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

Q: Find the derivative of f(x) = = 30 6/4x+1 Enclose numerators and denominators in parentheses. For…

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Q: Use Newton's method to approximate the given number correct to eight decimal places. √47 1.89969104…

A: Use Newton's method to approximate the given number correct to eight decimal places.476

Q: If f(x) = f'(x) = f'(4) = 4x + 7 2x + 3 find:

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Q: Question 1 [ 1 a. [ Use the method of multipliers to find the extreme value(s) of f(x, y) = x² + y2…

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Q: Find the function f(x) such that f'(x)=e^(3x)-6x+2 and f(0)=1. Thank you.

A: We need find the function f(x) such that f'(x)=e3x-6x+2 and f(0)=1

Q: If f(x) = (3x + 2)−ª, find ƒ'(x). Find f'(5).

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Q: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: Determine whether the series 2-√√n +∞o Σ √√n n=1 converges or diverges using the Integral Test.

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Q: Suppose that the position (a) Find the velocity at tin v(t) = 17 S (b) Find the velocity at tin

A: topic:- application  of derivatives

Q: - The equation of the sphere centered at C(h, k, l) and radius r is given by (x − h)² + (y − k)² +…

A: The given sphere equation x2+y2+z2-4x+2y+6z-11=0

Q: Find the average value have of the function h on the given interval. h(u) = (In(u))/u, [1, 6] have =…

A: The function is given as , hu=lnuu find the average value have on 1,6.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 - 3t, where 0 ≤ t ≤ 0.5…

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Q: If z = 5x2 + y2 and (x, y) changes from (1, 2) to (0.95, 2.1), compare the values of Δz and dz.…

A: We have to compare the values of Δz and dz.

Q: Graph the solution to the following inequality on the number line. x² +8x≥-12 Note that you ca…

A: First we will find the zeroes and then fix the interval.

Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

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Q: Let a-2-3j.kb-41-) and c-1-31-2k. If d is such that da-9. db-7 and dc-6, then d is equal to 01-31-2…

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Q: Let f g and h be the functions defined below i. 11. f(x) = 5¹ = 10x₁ (²² = 4) g(x) = log5 h(x) = 6 x…

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Q: Consider y=(3x^(2) +4)^(-5x)  Please find dy/dx and evaluate y'(0)

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Q: Graph the function showing all relative extreme points and inflection points. f(x)=√√√x6 + 4 ++ 2 3…

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Q: Evaluate the following definite integral. Express your answer in terms of logarithms. In 6 S In 5…

A: To evaluate: The integral ∫ln5ln6coshx4-sinh2xdx. Concept used: ∫1-v2+1dv=lnv+12-lnv-12

Q: A tank originally contains 100 gal of fresh water. Then water containing lb of salt per gallon is…

A: Basic differential equation is used

Q: Q5 a) 100 5² +2³+ [In(Inr)] lim 1+ 7 +6² + [In (In x)] 200 cos x ln(x - *) *-+*+ In (e² - e*) b) lim

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Q: For the differential equation y(n) + P₁(t)y(n-¹)+...+Pn(t)y=0 with solutions Yı, •, yn Abel's…

A: We have to find the Wronskian of a fundamental set of solutions of the differential equation.

Q: - lim x²ln x x->0+

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

Q: f(x( = (x( sinx

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Q: Problem 2.1 Find the vertical asymptotes of the function Then graph the function. Y x² +1 3x - 2x2

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Q: Rewrite the equation in exponential form.   ln(b)=n

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Q: Verify Gauss Divergence Theorem for F = xy²î + yx²j+ek for the solid region D bounded by z = √x² +…

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Q: Write a polar equation of a conic with the focus at the origin and the given data. parabola,…

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Q: Consider the function g(x) =−4 log (−1/3 (x + 2)) + 1. a) Describe, in order and with detail, the…

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Q: Find a bound on the magnitude of the error if we approximate √2 using the Taylor approximation of…

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Q: 4. Coffee at temperature 180°F is cooling in a room with constant temperature 75°F. If it takes for…

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Q: Describe the transformations that map the function y=2^x on the function y=2^x+3

A: Solution