Use L'Hospital's Rule to find the limit. Also, state why we can use this rule. lim(42x)³ln (4 - 2x) X-2

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A: This question is related to linear equations, we will solve it using given information.

Q: 38. 32 (-1)k k=0 (2k + 1)³

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Q: Use log, 20.401, log, 3≈ 0.503, and log, 5 0.794 to approximate the value of the given logarithm to…

A: Given : logb2≈.401 , logb3≈.503 and logb5≈.794 To find : logb75≈?

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A: First, we formulate a differential equation by using the given data and then solve it by using the…

Q: t Starting with an initial value of P(0) = 25, the population of a prairie dog community grows at a…

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Q: Let f(x) Calculate lim z→-5- lim 2-5+ (−4 − x)² +3 if x = -5 4x + 23 if x = -5 the following limits.…

A: Given  f(x) = (-4-x)2 +3 if x≠-5  4x+23       if x= -5

Q: Tutorial Exercise Find lim Ax-0 f(x + Ax) = f(x) Ax f(x) = 3x²-3x Step 1 Find f(x + Ax) by…

A: We will find the required limit.

Q: Find all roots of the polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs,…

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Q: The function f(x, y) = -2x² + 4y² - 11 has a local minimum at the point (0, 0). Select one: True…

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Q: Find the values of p for which the series is convergent. (Enter your answer as an inequality.) 00 Σ…

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Q: If cosa = 0.446 and cos 3 = 0.153 with both angles' terminal rays in Quadrant-I, find the following:…

A: cos(α+β) = cosαcosβ - sinαsinβsin(α-β) = sinαcosβ - cosαsinβ

Q: Next quest Solve the equation over the interval [0,2x), then support your solutions graphically. 2…

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Q: 1 with convergence in For the following problem, given that 1-x (-1,1), find the power series for…

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Q: Answer the following completely. f(x) = - sin (²1+5) +2 2 8 a. Determine the amplitude, period,…

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Q: For the curve defined by →r(t)=⟨e^−t,4t,e^t> find the unit tangent vector, unit normal vector,…

A: We have to find the unit tangent vector, unit normal vector, normal acceleration, and tangential…

Q: Find the limit. (If an answer does not exist, enter DNE.) x Ilm x-0 x² - 2x *2

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Q: Find both first partial derivatives. Lese fx(x, y) fy(x, y) f(x, y) = Com | Need Help? (5t +20) dt +…

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Q: Graph the function. y = log, x Plot four points and an asymptote. Then click on the graph icon. -9…

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Q: g(x) = cos ¹x+ 1-x

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Q: 1) .  Solve the initial-value problem with the initial condition y0 = 0. dy dt = y + 3 y =    graph…

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Q: Use Stokes’ Theorem to evaluate the flux integral ∫∫(∇×F)·ndS, where F =〈2y, −z, x+y −z〉, S is the…

A: To evaluate the flux.

Q: Find an equation for the graph sketched below -5 -4 -3 -2 -1 f(x) = 8 6 5 3 2 1 -1 -2 -3 -4 -5 -6…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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Q: Which one is the set of all critical points of the function f(x, y) = x²y + x² − 9y + 3? - Select…

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Q: sider the following. C: line segments from (0, 1) to (0, 16) and (0, 16) to (15, 15) (a) Find a…

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Q: Let R be the region bounded by the following curves. Use the method of your choice to find the…

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Q: A radioactive isotope has a half life of 1 min. The amount of material, A(t), at t = 0 is 10 kg.…

A: A radioactive isotopte has a half life of 1 min. The amount of meterial, At, at t=0 to 10 kg.To…

Q: Can you please write it out I can't read it typed.

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Q: Find the solution to y' =    2y satisfying y(0) = 15.       PLZ SHOW STEPS

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Q: nt The formula A = P 1 + describes the accumulated value, A, of a sum of money, P, the principal,…

A: Use given formula

Q: Find the displacement of an object on the interval 0 ≤ t ≤ 6 if its velocity is v (t) = 4t -√√t

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Q: Ind the one-sided limit (if it 1 Ilm *--5+X+5

A: topic:-  limits

Q: Suppose a population of P(t) satisfies dP dt 0.4P - 0.001P² P(0) = 50 a What is the carrying…

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Q: Find the constant a such that the function is continuous on the entire real line. (sx, lax 9₁ a=…

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: The population of a city is modeled by the equation  P(t)=449,512e^0.25t where t is measured in…

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Q: . Use separation of variables to solve the differential equation explicitly for u. du dt = 4 + 4u +…

A: topic:- differential equation

Q: Solve the given differential equation. ex²dy=x√/10-y dx Choose the correct answer below. OA. 4√/10-y…

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Q: Tutorial Exercise Use the position function s(t) = -4.9t² + 750, which gives the height (In meters)…

A: Let's find the value.

Q: Find the coordinates of a point on a circle with radius 25 corresponding to an angle of 135∘ (x,y)…

A: We have to find out the coordinates

Q: Suppose d(10!*x) = 2700, here x is another integer. What is the minimum possible value of x? Here…

A: given : Suppose d(10!*x) = 2700, here x is another integer and  gcd(10!, x) =1.

Q: For the function, locate any absolute extreme points over the given interval. (Round your answers to…

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Q: Find the Taylor polynomial 7₂ for the function 3 O3+ (x-1)+(x-1)² 54 f(x)=√8+

A: We have to find the Taylor polynomial for the function f(x) at the number a=1. And power series…

Q: Find the solution to y' =    2y satisfying y(0) = 15.

A: Solve the following

Q: The rate of change of R is inversely proportional to R(x) where R > 0. If R(0) = 25, and R(4) = 10,…

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Q: 4 -15 Given sin A = and sin B 5 17 match each expression in Column 1 with its exact value in Column…

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Q: ← Write the expression as an algebraic expression in u, u > 0). cos sin cos sin 1 1 2 2 = (Simplify…

A: We will find the solution

Q: Question Rewrite the following quadratic function in standard (vertex) form. Enter exact values and…

A: This is a problem related to application of algebra. Please follow the procedure given below.