Consider the following function. f(x) = 2x² Find the limit. lim f (x + Ar) - f (x)

Q: Determine f(5) if f is a continuous function that satisfies +sin(a) f+sin(a) f(t)dt = 22² for all x.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Explain why lim F(x) in Figure A exists, but lim f(x) in Figure B does not. X-2 X→-2 Figure A AF(x)…

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Q: Find Domain and Range y=-ex-1 The domain is (-00,00) and range is (-00,0) The domain is (0,00) and…

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Q: 1. Determine (i) the order of each differential equation and (ii) whether they are linear or…

A: Given differential equations are  y4+y2+y=sint  y''+yy'=1

Q: Question Find the area, in square units, of the region bounded on the left by the line g(x) = 2x +…

A: We need to find Area.

Q: Find all minors and cofactors of the matrix. -1 2 3 6 45 3-1 2 (a) Find all minors of the matrix M…

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Q: The graph is a transformation of one of the basic functions. Find the equation that defines the…

A: We can find the answer as below.

Q: eff(x) da, where Evaluate S²1(²² f(x) dx = 0 f(x) = [8x¹, (3 sin(x), -π<x<0 0≤x≤R.

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Q: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: what points on the given curve  x = 2t3, y = 5 + 50t − 10t2  does the tangent line have slope 1?…

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Q: Use the cross product to find the area of the triangle with the vertices P = (1, 1,5), Q = (3, 4,…

A: NOTE: Refresh your page if you can't see any equations. . given 3 points are

Q: Consider the following. f(x) = (fog)(x) = X # (a) Find the function (fog)(x). I Find the domain of…

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Q: 3300t The system of the population of a culture of tumor cells is given by p(t) = t+1 Select the…

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Q: The given vectors form a basis for a subspace W of R³. Apply the Gram-Schmidt Process to obtain an…

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Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

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Q: Find each of the following for f(x) = 4x² - 7x+ 5. (A) f(x + h) (B) f(x+h)-f(x) (C) f(x+h)-f(x) h

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Q: Given the integral: fcos-¹ 1 x dx

A: Given :    Integral : cos-1(x) dx

Q: An integrand involving a radical form 49-16x2 suggests the substitution

A: Given: fx=49-16x2 Let, I=∫49-16x2dx   ....(1)   As we know the trigonometric identity; 1).…

Q: ¹{.(²-1)} = Q4. C-1 (a) cosht - 1 (b) (c) 1 2 (d) 1 - cosh t [cos 2t - 1] [sin 2t - 1]

A: Here, to find the inverse Laplace transform of the function: 1s(s2-1)=1s(s-1)(s+1) Now, using…

Q: Q5/: Find the general solution of non-homogenous differential equation using Variation of Parameters…

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Q: Consider the series 6+4 6n³-6n+8 n= We will try to use the ratio test to determine whether this…

A: To use ratio test to determine whether the given series converges or diverges

Q: 4 Find the roots of Z²+1=0 itt/2 Hint i = e 3

A: Given z4+1=0

Q: 20. What is the probability of an actually event? a. 0 O b. Insufficient data O C. 1 O d. Not…

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Q: - 3 f(x)= x-2 2 if x 4 (a) Choose the correct graph below. ITPT▬▬ O Te C T ▬▬▬▬▬▬▬ Q O CHH do #fo 2…

A: Topic:- function

Q: he probability distribution for the rando ariable, x, is x:2, 2.5,3.0,3.5,4.0,4.5 and (x):0.07,…

A: Topic:- application of probability

Q: 35. [T] lim sin2x; ±0.1, +0.01, +0.001, +.0001 *40 X X -0.1 -0.01 -0.001 -0.0001 sin 2x a. b. d. X…

A: The answer is given below:

Q: fk(x) = x³ +512 X+8 X k(x) 2 complete the table and use the results to find lim k(x). X→-8 - 8.1…

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Q: Book Problem 31 Find a function f and a positive number a such that f(x): a = = + [² 2+ f(t) dt =…

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Q: Book Problem 1 Sketch the graph of the function f(x) = Let g(x) = f(t)dt. (a) Then g(-6) = g(-3) =…

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Q: A torus is formed by revolving the region bounded by the circle x2(squared) +y2(squared) = 4…

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Q: 7 ♡ Ņ T 2 0 -1 -2 y-intercept x-intercept Return this question to its initial state 3₂2 Drag the…

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Q: Let lim f(x) = 19 and lim g(x)= 16. Use the limit rules to find the following limit. X-9 X-9 lim…

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Q: variable, x, is x:2, 0.36, 0.21, 0.19, 0.10, 0.07 Calculate P(x >= 3.0) a. 0.47 O O b. 0.83 019…

A: Topic:- probability

Q: Determine the flux of D = p² cos² þap + z sin ☀ a over the closed surface of the cyl- inder 0 ≤ z ≤…

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Q: The probability a machine has a lifespan of more than 5 years is 0.8. Ten machines are chosen at…

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Q: 1. The graph of f '(x) is continuous and increasing with an x-intercept at x = 4. Which of the…

A: Let's solve.

Q: Solve 273 (Q)dx if Q=0.85x² + 6x + 12 298

A: Given :∫298273QdxQ=0.85x2+6x+12

Q: Question Find the area, in square units, of the region bounded on the left by the line g(x) = 2x +…

A: The objective of the question is determine the area bounded by the given function.

Q: In how many ways can we of 12, of which a particula included? a. 904

A: Topic:- permutation and combinations

Q: Electricity rates. The table to the right shows the electricity rates charged by Better Than…

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Q: d (19) dx [xy] dx

A: We have to find the integral.

Q: Determine the area, in square units, of the region bounded on the right by the line g(x) = -3x+27,…

A: Given thatgx=-3x+27fx =-x-52+16To find: Area bounded by the region with respect to y.Note: right to…

Q: random variable, y, has a known probability distribution given by Y :2,4,6,8,10 and P 0.17,0.23,…

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Q: Calculate the means and standard deviations of:1, 2, 3, 4, 5 O a. a. mean = 3; st. dev. = 1.414 O b.…

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Q: X Given zx 2cos u; y = 3sin v, find y O-2cos u cos v 3 sin ² v O 2sin v 3 sin u O-2sin u 3 sin v…

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Q: Find the roots of Z₁ + 1 = 0 Hint i = 1/2 e

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Q: x² (d) S √1-4x² (HINT: sin² t = dx. (1. (1 - cos 2t).)

A: We have to evaluate ∫x21-4x2 dx.

Q: Sketched below are the graphs of f(x)=x²-1 and g(x)=x+1., The graph of fintersects the x- axis at A…

A: Given data:- The given equation, f(x)=x2-1g(x)=x+1

Q: Given: f(x)+ 3x2+1, Evaluate the difference quotient for f(x+h)-f(x)/h; h≠0

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Q: 2. Solve the initial value problem x' = (t+1)/√t, x(1) = 4.

A: Given, x'=t+1t, x(1)=4