If f(x) = (1 + 3), find lim f(x). 6x 0-x

Q: Evaluate the following indefinite integrals. cos(tan-¹) 1+x² (a) [ (b) / tan³ z dr. dx.

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = 5x4 - 20x³ +6

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Q: Find A A = OA. A Select the correct choice below and, if necessary, fill in the answer boxes to…

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Q: Q4.5 If f(x)= e2x O e²x - √xe² e4x 1 4e²√√x 4√xе²x then f'(x) = x 1/2e2x -x 2e4x O 1 - 4x 2e2x √√√x…

A: Need to find out the derivative of the given function.

Q: 10" n=1(n+1)42n+1 Consider the series Answer: L = Evaluate the the following limit. If it is…

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Q: 2. The Laplace transform of ƒ is defined by f f(t)e-st dt. -6 F(s) = for Let f(t) = sint, find F(s).…

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Q: Determine, without solving the equation, the interval where the solution is guaranteed to exist for…

A: NOTE: Refresh your page if you can't see any equations. . the given DE is  divide both sides by

Q: 85,000 is deposited in a saving account with 6.35% annual interest. When will be the initial sum…

A: To solve this problem, we can use the formula for compound interest:

Q: Evaluate the indefinite integral as a power series. 1 f(t) = 8 f(t) = C + Σ Ë n = 1 In(1-t) dt 4t…

A: Give function:- ft=∫ln1-t4tdt

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one…

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = ti…

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Q: Find the values of c which satisfy the conclusion of the Mean Value Theorem on the given interval,…

A: The given function: rx=x-5 on -12,8.

Q: Consider the solid bounded below by the xy-plane, on the sides by the sphere p=5, and above by the…

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Q: Find y as a function of a if y" - 14y" +48y' = 70e", y(0) = 12, y'(0) = 29, y" (0) = 28. y(x) =…

A: Given: Here, the characteristic equation is     m3-14m2+48m=0. Now,…

Q: Use the function h(x) = = x². 7x to answer the questions below. (a) Is h(x) a one-to-one function?…

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Q: Use the substitution y=x' to find a general solution to the given equation for d²y 2 dx² 3 dy x dx…

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Q: Find the absolute minimum and absolute maximum values of f on the given interval. Hint: You will…

A: Given function:-   ft=4cost+2sin2t

Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

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Q: Consider the graph of a function f. y X Identify the correct statements about the graph. f"(x) > 0…

A: Please see the below answer.

Q: Write the expression as the logarithm of a single quantity. 1/2 ln(x) + 6 ln(y) − 3 ln(z)

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Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: Solve the​ triangle, if possible. a = 100 m, A = 13.15°, C = 27.07°. Find if there is one or more…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: T The region bounded by the x-axis and the part of the graph of y = cos x between x = - 2 T of the…

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

Q: (9) (a) Find the equation of the tangent plane P to the paraboloid z = = x² + y² at (1, 2,5). (b)…

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Q: Let f(x)=x²-c² and g(x) = c²-x² Find c> 0 such that the area of the region enclosed by the parabolas…

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Q: Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time.…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x³ - 6x² -…

A: Given that  f(x) = 4x3 -6x2 -144x +3. ; [-4,5]  We find absolute minimum and maximum value.…

Q: (8) A manufacturer wants to make an open box of volume V 500 cubic cen- timeters using the least…

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Q: D Question 5 D The table gives selected values of the continuous function f. 7 8 9 10 f(z) -11 -10…

A: Note: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b]…

Q: (10) Show that the following limits do not exist. (0,0) (b) lim y³ +2³ (p) (0,0) ry²

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Q: Use the laws of logarithms to expand and simplify the expression. ln (x(x + 5)(x + 6))

A: Given

Q: 6. If f(1) = 10 and f'(x) ≥ 2 for 1 ≤ x ≤ 4, how small can f(4) possibly be? Hint: Apply the Mean…

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Q: Evaluate each of the following indefinite integrals.  ∫e2xsin3xdx

A: Answer is in step 2.

Q: 3t Find the linearization L(x) of f(x) = cotx at x = 4 The linearization is given by L(x) = Type an…

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Q: 1. Evaluate: a. -1 b. -2 sin³ x lim x-0 sin x-tan x C. 0 d. 1

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Q: what do the following quantities represent? (a) f(20000) ---Select--- cost of building a store of…

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Q: For the function y = f(x) = x² - 2x - 3, x ≥ 1, find (f¹)'(-3)= df 1 dy ly 3

A: We can solve this as follows:

Q: Fill in the missing values such that the final term is pulled out of the summation. Ex: 5 15 Σ; = Σ…

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Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A: Given function  h( x ) =  x3 + 3x2 + 5

Q: Find parametric equations of the line through (-2, 1, 4) that is parallel to 5 i-8j+k. x(t) = y(t) =…

A: The line is passing through the point  x0, y0, z0 = -2, 1, 4 The line is parallel to the vector…

Q: 2) Find the local maximum and minimum values and the saddle points of the inction f(x, y) = x² + y²¹…

A: Please see the below picture for detailed solution.

Q: 5 Given that f(x)=x²-x² - 2x + 1, find the coordinates of all the points where f(x) has a horizontal…

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Q: Find g[f(-2)]. f(x)=x² +4; g(x)=4x-1 g[f(-2)] = (Simplify your answer.)

A: Given: f(x)=x2+4; g(x)=4x-1

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: The given function is: f(x)=2x3-11x2+1

Q: Find the values of c which satisfy the conclusion of the Mean Value Theorem on the given interval,…

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Q: Absorption of Drugs The concentration of a drug in an organ t seconds after it has been administered…

A: The concentration of a drug in an organ t seconds after it has been administered is given by  x( t )…

Q: dy Look for the of ysinhx = sec ¹ (tanh-¹x) — dx In solving, use exponentiation

A: Given equation:- ysinhx=sec-1tanh-1x

Q: Approximate the sum of the series correct to four decimal places. (-1)^ 4^n! S≈ 00 n = 1

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Q: 1. Determine the following, if g = [3, -2,5] and h = [4, 1, −6]. a) g + h b) g- h c) g.h d) Igl

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

Q: f(x) = -3 sin T2 - 2bx² x -2 x 3x² + e²

A: Please see the below picture for detailed solution.