6.1. Determine the values of m and n so that the function f(x) will be continuous for all values of x: mx-n, if xs-1 f(x)=2x² + 3mx+n, if-1 1

Q: 11. If f(x) = cosh-1(5x), then f'(x) = A) 5 25x²+1 B) 5 25x²+1 C) 1 √25x²+1 D) 5 √√25x²-1 E)…

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Q: 7. Find the area under the first arch of the curve y = x sinx.

A: I have stated the used formulas in the solution

Q: Eliminate the constant: =c₁e²x+c₂e³ 3x

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Q: Use integration by parts to evaluate the definite integral Answer: te-t dt.

A: Given  that ∫06te-tdt.To evaluate : the definite integral.Solution :∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx…

Q: Function Properties Sketch a function that meets the following criteria and upload it. • Domain is…

A: Solution of given question is written in below steps.

Q: In Problems 7-10, xc₁ cost + co sin t is a two-parameter family of solutions of the second-order DE…

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Q: families of curves straight lines with slope and x-intercept equal

A: Here is the solution:

Q: 2) g(t)=3t+4; Find g(-3) 2) (200)- 5.2-3 Find - 4) w(x) = -3x - 4; Find w(7)

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Q: Use integration by parts to find the following: [(t+ 7)e²²+3 dt = | 2t+3 t=+C

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Q: Find the center and radius of the circle. (x + 5)2 + (y - 3)² = 4 (x, y) = ( center radius Cleotab…

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Q: 23. fsin(Inx) dx = x A) cos(In x) + c. B)-cos(In x) + c. C) sin(lnx) + c. D) -sin(In x) + c. E) -cos…

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Q: (A) Let x represent the number of years since 1980 and find a cubic regression polynomial for the…

A: This is a problem related to regression fitting of curve. Please follow the procedure given below.…

Q: H(x)=x^3-64/x^2-9x+20 Find the vertical asymptotes: Find the oblique asymtotes: How do you solve…

A: You must have proper understanding of limit of functions and how they behave for different values of…

Q: 4. Set up an integral for the arc length of f(x) = 2ª + x² on [0, 1]. Do not evaluate the integral.

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Q: Consider the following general term for a sequence an 3(4)" What are the first five terms of the…

A: Consider the following general term for a sequence an=34nTo determine the first five terms of the…

Q: Using the following graph of the function f, evaluate the limits (a) through (i). Q to h Ay O (a)…

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Q: 13-16 Use the definition of continuity and the properties of limits to show that the function is…

A: Use continuity concept

Q: Q13 If S, 4+ is the nth partial sum for the infinite series find the value of ay A) - B)-- (C)- D)…

A: We can solve this as follows:

Q: x + y + z x+y=4z = -4x+y+ z LO 5 10 0

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Q: Q 7 please

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Q: 1. Find d for the following implicit function: cos([y(x)]²+ 1) = 2x. Note: y(x) means that y is a…

A: To find out the derivative dydx.

Q: Find the x- and y-intercepts of the graph of the equation. (If an y = x² - 2 x-intercepts…

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Q: Use the discriminant to determine all values of k which would result in the equation -x^2+kx-25=0−x…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is compare this…

Q: 15. Given that f(x) = x Warnin ₁,8(x) = g(x)= =, h(x) = x² - 1 1' X x- find a formula for fogoh and…

A: We can solve question no 15 as below.

Q: Instructions: In each of the following, eliminate the arbitrary constants. 1. cx² + y² + x = 0

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Q: Q12 Find (3 in)) is: A)-300) sin(x) B) 3x) cosx ln(3) C)-3(3) sin(x) D) 3

A: 12). The given function is; fx=3sinx   As we know the Chain rule: fgx'=f'gx·g'x And the common…

Q: Find the x-value at which f is discontinuous and determine whether f is continuous from the right,…

A: Please see the below picture for detailed solution.

Q: B: Find y + 4 lim (x1)-(24) x²y-xy + 4x² - 4x

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Q: Sketch the graph of the function by first making a table of values. k(x) = ³√/-x X -27 -8 -1 0 1 8…

A: Let's sketch the graph of given function.

Q: A. Identify the type and determine the linearity of the given differential equation and also give…

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Q: Find the x- and y-intercepts of the graph of the equation. (If an 9x² - y² = 144 (x, y) =…

A: The given equation is 9x2-y2=144 To find: we have to find the x and y intercepts of the graph.

Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x)=x² + 4x-9 f'(x)…

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Q: a) Find the Laplace Transforms of i. t²u(t-1) te-3tu(t) cos² (wt)u(t). ii. iii.

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Q: 5. [8.1.11] Find the arc length of f(x) = ²3³ + 1/ on [1, 2] exactly. (Hint: try to express…

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Q: Find A and B given f(x) = (3Ax² + 2Bx-x³ 3A - x-1 (5Bx + +4-3A x≤2 is differentiable everywhere. x>2

A: NOTE: Refresh your page if you can't see any equations. . it is given that the function is…

Q: tanx 7. f(x)= x²-3

A: The function is  f(x)=tanxx2-3

Q: The values of x, y for the following matrix equation are x-2y -2 X = 05 06 03 3 0 ]-[-²2₂ 6] [-2…

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Q: -5 -4 -3 1 In the above graph of y = (3, ƒ(3)). 4 3 2 -3 4 -54 f(x), find the slope of the secant…

A: Topic- Slope of a secant line we are given two points on the graph as (-3,f(-3)) and (3,f(3))…

Q: Write down the first five terms of the following recursively defined sequence. a1 = a₁ = a2 a3 || ||…

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Q: Solve the Differential Equation using Method of Undetermined Coefficient d²x dt² -2 dx dt + 3x = + ²…

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Q: cosx if x0 23. f(x)-0 4-0

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Q: I. Write TRUE if the statement is correct and FALSE if not. 1. {0} - Ø 2. (0,1,2) and () are joint…

A: Solution is given below:

Q: The values of x, y for the following matrix equation are 3 0 1-[-²2 x+y] ₂] x-2y 0 -2

A: Concept: First equate the column elements of the matrix on each side  Forming the two equations…

Q: 12. Let f(x) = -x² and g(x) = 1/√x. and go f and state the domain of each composition. 13. Given…

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Q: a/the derivative of the following function is y=x²-sin x

A: Solution )  y = x2 - sin x  Differentiate with respect to x  dy/dx = d/dx( x2) - d/dx ( sin x )  […

Q: Obtain general solution of this differential equation (2xy-y)dx+(x^2+x)dy=0

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Q: Can

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Q: Transform the differential equation y'e yer = 2xy² to FOBDE form. I O dy da O dy da - y = 2xe-y² dy…

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Q: eliminating arbitrary constant y= C1 cos 2x + C2 sin 2x

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Q: 18 f(x) = x + 2x -1.find (fY(-1) A) S B) 2 앞 -IN

A: I have appended the formula used in solution part.