Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n = 2x - - - 5 nx - m - n if if if x < 2 2 < x < 4 x > 4

Q: (x² − 5)· 4x³ − (x¹ − 4)· 2x (x²-5)² f'(x) = Find f'(2).

A: We wil find the required.

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A:

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

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A: Given, an=3n1+4n

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A:

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A:

Q: 5. lim -00 2-1 5

A: limx→-∞x2-x45

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A: We need to find velocity and distance.

Q: x/4 11. evaluate sec(x) dx . Give 3 decimal places for your answer. If your answer is below 1, use a…

A: ∫0π4secxdx

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A:

Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 8, t > 0 y =

A: This differential equation can be solved as follows:

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 the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) [39] 163-

A: find the inverse of matrix= 30   04

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

A:

Q: Solve the system below. Parameterize the solution set. x - 5y + 2z 5y + X 9z 4z - - - 3w 24w 12w - -…

A: The given system of equations, x-5y+2z-3w-u=0x-5y+9z-24w-3u=-14z-12w-u=-1

Q: question 5. (D² + 4D + 4)y=0, x= 0: y = 1, y' = -1 answer 5. y = e 2x (x + 1)

A:

Q: Suppose f and g are continuous functions such that g(4) = 2 and lim [3f(x) + f(x)g(x)] = 10. Find…

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Q: 12x5y² 9. Simplify, stating your answer using positive exponents: -3x³y

A: The expression is given by 12x5y2-3x3y To determine: The simplified expression of the given…

Q: 7. State the restrictions on f(x) 2x 3x-6

A:

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A: ∫01/2 IN (1-x dx - ∫0xdx

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A:

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A:

Q: Solve for x, y, z, and win the matrix equation (X, Y, Z, W) wx 2 {]+=[xx]-

A:

Q: 11. Prove the identity: tan²x tan²x + 1 = sin²x

A: Simplification

Q: Simplify: 3√2 + √32

A: Given.

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A:

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A: Given thatRegion bounded by y=x28 , y=3xx=1 and x=3Using cylindrical shell mathod…

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Q: Using continuity, evaluate the limit: - 1 sin(z + sin(x)) lim X→ -

A: Topic- Limits

Q: . Test the equation for symmetry. (Select all that apply.) y = 7x4 + 2x2 a. The graph is symmetric…

A: Topic = Function As per guidelines , At a time only one question with three sub-parts can be…

Q: 14. Estimate the area under y = 36-x² using 3 rectangles and the left endpoint method. y=M-2²…

A: Here we use the left endpoint method.

Q: If f(x) = (cos(√) - In (x²))³, then f'(x) = 3

A:

Q: 2. Graph the function y=2-x, x = 0 √x, x>0 Determine the domain and range.

A:

Q: 20. f(x) = sin a for a < 0 cos x for 0≤x≤ ³T tanx for 37 < x < 2π for 27 < x < 5 cot a Let f be the…

A: A piecewise continuous function is continuous on a given interval in its domain if the function…

Q: 7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

A: NOTE: Refresh your page if you can't see any equations. . take x=e

Q: 1. Determine the domain and range of the following functions: (Note that each square is 1 square…

A: To find the domain and range of the functions in the given graphs.

Q: 2. y' ysecx

A:

Q: Use the spreadsheet to answer the following questions. 83 123 45 A 45848 Answer: 47 37 94 76 60 B ✓…

A: We can solve the given question as follows:

Q: 17. For an object whose velocity, in ft/sec is given by v(t) = 2sin(t), what is its distance, in…

A:

Q: The point P(1, 0) lies on the curve y = sin( 13 (a) If Q is the point (x, sin(¹3″ )), find the slope…

A: Note :- “Since you have posted a question with multiple sub-parts, we will solve first three…

Q: integral: 24x² √64 – x² dx

A: ∫ 24x264-x2dx

Q: Need this in complete and handwritten solution, thank you! 3. Solve for the Homogenous Differential…

A: Ode

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A: Here we have to find the value of x for which f is discontinuous and determine whether f is…

Q: If f¹ f(x) dx = 3 and 5 f¹ f(x) dx = 25, then ff(x) dx A)-2 B)1 C)-1 D) 2 E) 8

A: We have ∫3-1f(x)dx=3, 5∫31f(x)dx=25  We have to find ∫-11f(x)dx=?

Q: 4. Find the surface area when the function y= 6 + 1 2x on the interval 1≤x≤2.

A:

Q: A differential equation is an equation A that contains a derivative like y'(x) as well as the…

A: