Given the piecewise function below, find the value of k which makes the function continuous. f(x) = k - 2x if x < -2 if x ≥ −2 −x+4

Q: 2 ft²cos nлtdt

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Q: Which of the following functions represents the graph of f(x)=√x+1-2? 6 5 4 3 2 f(x) -10 6 7 -1 O O…

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Q: Solve the initial value problem. 1. y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

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Q: If acceleration is a(t) = sin(t) and initial velocity is v(0) = 3, what is an integral function that…

A: topic- integration

Q: 4x 10. Find all vertical asymptotes for the rational function f(x) = x²-144 11. Find all of the…

A: We can solve this as follows:

Q: of the 3. Find the de AND FINAL ANSWER 1. f(x) = (4x² +8x + 2)² 2. f(x)=(2x +6) f(x)=(3x²+2x+1)³ 3.…

A: Topic = Derivative

Q: Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in…

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Q: a) Find the root of the equation f(x) = 2cosx-x² to 2 decimal places using the Newton-Raphson…

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Q: Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.)…

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Q: [t²cos n=tdt 2 Solve the integration by table or zeroing method, then arrange the integral and the…

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Q: If f(t) = sin−¹(3t), find ƒ'(t). Use exact values. ƒ'(t) =

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Q: integral (Integration by parte ) [xln x

A: We will solve the problem

Q: Given cost and price (demand) functions C(q) = 100q+43,000 and p(q) = -1.9q +880, how many items…

A: Given problem:- Given cost and price (demand) functions C(q) = 100q+43,000 and p(q) = - 1.9q + 880…

Q: Match each equation with the graph of f, g, h, or k in the figure. (A) y = 6* (B) y = (0.6)* (C) y =…

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Q: 4.[(5x³ 5.Ĵ(6x² − 2x² +4x)dx − 3x+1)dx

A: Topic = Derivative

Q: A. Find the determonant of the matrix A = 1 2 1 -21 -1 -2 -1 4 2 132 L-2 1 2 -3

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Q: Find each x-value at which f is discontinuous and for each x-value, determine whether f is…

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Q: Considering the definition of f(x) below, find lim f(x). x→6 f(x) = -2x² + 3x - 2 -x²-x-2 -x² +1 if…

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Q: Suppose z is a function of r and y, and x² + y² + z² = xe² + ye² + ze³. Solve əz əz for and əx ду

A: Topic = Derivative

Q: 6- Do a complete analysis to sketch the following function. F(x)=2x-x²/x²-2x+1

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Q: FOR NUMBERS 6-7 Tangent and normal lines are drawn to the curve y = x3 at x = 2, 6. What is the…

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Q: Find the equation for any horizontal asymptotes for the function below. f(x) = 5-8x+x² 4+5x+2x²2² CO…

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Q: A can is dripping out water at a rate of r(t) = 12/17 If the can held 50 cm³ of water at time t = 1,…

A: If rt is the rate of dripping out water from a can then volue of water dripping out after t time is…

Q: Evaluate the iterated integral y² T² (4x+10y) dxdy. 0 O O 11 10 0 -1 O 1 O All of the above Y 11 10…

A: Given query is to find the value of the integral.

Q: 0 1 S -8 (2x-1)3 -dx

A: ∫-∞0 12x-13dx

Q: Suppose

A: We will solve the problem.

Q: Question 5 Use Pascal's triangle to expand your binomial expression. A (1 + x)³ B (1-x)³ C (1 + x)4…

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Q: Determine whether the differential equation (3x + 8) + (3y − 3)y' = 0 is exact. If it is exact, find…

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Q: S 8-3x (x+1)(x² − 4x+6) - dx

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Q: Q4. Let R be the region shown in the accompanying figure. Evaluate the following integral by…

A: Explanation of the answer is as follows

Q: 1. Which of the following is the reverse operation of [f(x)]? dx A) f f(x) dx B) Jdx C)f cdx D) dx…

A: Topic = Integration 1) A 2) A

Q: R: y = 6x x² and y = x² - 2x.

A: Let's find Area of region.

Q: 1. Given that a right triangle has sin 0 = 0.5. Find another two sides of length if hypotenuse…

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Q: 8) Consider the solid Q that is generated in the first octant by the surfaces S₁: (x - 2)² + (y-2)²…

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Q: A population of 470 bacteria is introduced into a culture and grows in number according to the…

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

A: solution:-f(x)=x2-4x-5x+2,    -1, 5f(x) is continuous in  -1, 5f'(x)=x+2ddxx2-4x-5-x2-4x-5ddxx+2x+22…

Q: Which of the following conditions is NOT required for lim f(x) to exist? x→a

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Q: A graphing calculator is recommended. If a ball is thrown into the air with an initial velocity of…

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Q: A cube with sides 15 inches long is covered with a coat of fiberglass 0.2 inch thick. Use…

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Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²)+1 at…

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Q: Suppose c is a real number, which of the following limits ALWAYS exist?

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Q: Total claims rejected: 100 Total claims submitted: 1,000 Time period: 3 months   Calculate the…

A: Rejection rate

Q: 1. Given the function f(x) = sinx,x=(0,2€). Please find the intervals of increase or decrease, local…

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Q: Solve the ff initial value problem. 1. y'=4xe2x²cosx - ytan x, where y(0)=1 2. y'=e-2x y², where…

A: To solve the Initial Value Problem:

Q: Q2 Q1 Find the points of intersection of the polar curves r-cos = 0 and 2-cos -r=0

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Velocity is obtained by differentiating f(t)

Q: y =(3+5.x)" Use Logarithmic Differentiation to find dy da dy dx

A: topic- logarithmic differentiation

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: The answer is given below:

Q: Question 5 Use Pascal's triangle to expand your binomial expression. A (1 + x)³ (1-x)³ (1 + x)4…

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Q: Problem 9. Find absolute extreme values for (2) g(t)= = √t 1+t²⁹ x = [0,2].

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