x² x-o ex-x-1 Evaluate lim А A) 0 B) 1 C) 2 D ∞ by applying L'Hôpital's rule.

Q: Suppose f(x) = 6 - x². (a) Find the slope of the tangent line to the graph y = f(x) when x = 2.…

A: a) f(x)=6-x2…

Q: 12. y' = x² - 2xy + y²

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Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

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Q: 3. Write down the name of the conic given by the polar curve r = 6/(2-sine). Determine the vertices…

A: Given problem:- 3Write down the name of the conic given by the polar curve r = 6/(2-sin(θ))…

Q: f the function. [(x, y) = x²y³ + x, t) = √√√x In r =tan xy (x, y) = x² = e²/(u + 11²)

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Q: Blologist is monitoring the population of a rare species of Jackelope. The initial population size…

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Q: s = t³ - 8t² + 2t, t≥ 0, where t is measured in seconds and s in feet. (a) Find the average velocity…

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find the absolute maximum and absolute minimum values of the function, if they exist, over the…

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Q: Consider the following function. f(x) = x¹/⁹ + 8 (a) Find the critical numbers of f. (Enter your…

A: We will apply f'(x) =0 to get critical number.    If f'(x) > 0 for all x in an interval then f(x)…

Q: . Orthogonal Trajectories y = C (sec x + tan x) Oy² = 2 (C -sin x) 2y = (Csin x)²

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. +9 So. || 4 + 12² || ll ti 247.18 dt =…

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Q: b) y= x(x-2)(x+1), y X

A: We have to find out

Q: 10) The marginal profit from producing x widgets is given by P'(x) = 72,600e-0.12x. Suppose it were…

A: Given query is to find the total profit.

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y=4-x² b.…

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Q: Protected ViewSaved to this PC Search (Alt+Q) Mailings Review View Help 8-9. You want to have…

A: The compounded continuously formula is A=Pe^(rt) Where A= amount  P= principal  r= rate t= time

Q: Determine the average cost function C(x)= C(x)=x²+2x²-3x+40 Determine the average cost function.…

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Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: t Starting with an initial value of P(0) = 30, the population of a prairie dog community grows at a…

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 4x6_ X lim x →∞0 x³ +9

A: We need to evaluate the following limit limx→∞4x6-xx3+9

Q: Find the first four non-zero terms of the Maclaurin series for f(x) = sin(x²) cos(x²).

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Q: Evaluating a Definite Integral In Exercises 67-74 evaluate the definite integral. Use a graphing…

A: We want to evaluate the integral.

Q: Write the first four terms of the sequence whose general term is given. 2n an n+1

A: Given: an = 2nn+1 To find the a1, a2, a3, a4 substitute 1, 2, 3, 4 respectively in place of n

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use ∞o…

A: The detailed solution is given below Thank you

Q: Determine whether the sequence converges or diverges. If it converges, compute the limit.    an =…

A: Use ratio test

Q: 60.) f(x, t) = x²e¯¤¹; fm, fixx

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Q: ch a graph of the function. in the piecewise definition f(x)= v the graph of f. --6-5-3-2 lear All…

A: We will graph the function.

Q: Find the center and radius of a sphere with the equation: 8x + 4z = 1 − 2x^2 + 20y − 2y^2 − 2z^2.

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Q: T 1-2² (a) This is true. (b) This is false. 8. dr = arcsinz+C

A: Solution: ∫π1-x2dxTake constant out:=π·∫11-x2dx

Q: Use the given vectors u and v to find the magnitudes of vectors u - v and -2u. u =4i+6j+7k, v = -i…

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Q: SHOW ALL WORK Change the polar coordinates, (r, 8) to rectangular coordinates, (x, y). (Leave…

A: Given the query is to find the rectangular coordinates.

Q: Applying the First Derivative Test In Exercises 29-36, (a) find the critical numbers of the function…

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Q: Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c…

A: Here, the given function is: f(x)=4-x23

Q: Determine whether the series is convergent or divergent. If the series is convergent determine the…

A: Given problem:-

Q: The position function of a particle is given by s = 2t³ - 9t² - 100t, t> 0. where s is measured in…

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Q: A "bead" is formed by removing a cylinder of radius r from the center of a sphere of radius R (see…

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Q: Q2):- Find Y[Z] of signal Y[n] (Cos wn). U[n]

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Q: summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

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Q: 5. SHOW ALL WORK Find the six trigonometric functions of 0 given the triangle shown below. A 0 (5)…

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Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Given problem:- A manufacturer has determined that the total cost C of operating a factory is   C =…

Q: 16. f(x, y) = x+y³ + 8x²y

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Q: Solve the right triangle using the information given. Round answers to two decimal places, if…

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Q: For the polynomial g(x) = x³ − 5x² + 5x + 3 - Express g (x) as a product of linear factors. below, 3…

A: Use the zero given for finding out the factor

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Ordinary differential equation dx/dy = ( x-e-x )/( y+ey )

A: We can solve as follows

Q: If "6 fº 181 f(x) dx = 37 and 6 √° g(x g(x) dx = 12, find 6° 1² [3f(x) + 5g(x)] dx.

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Q: Let f(x) = 2x³ + 1. a) Find f(x + h): b) Find f(x + h) − f(x): c) Find_f(x+h)-f(x). h d) Find f'(x):…

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Q: Use algebraic and/or graphical methods to solve the inequality. 91 - 13x > 13 X

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Q: The function v(t) = t³ - 5t² + 6t, [0,5], is the velocity in m/sec of a particle moving along the…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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