3 - 2x? +x- 2 Use L'Hopital's Rule to evaluate Support your answer graphically. lim X2 x² +x-6

Q: e 4x =dx e4x – e

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Q: fourth-degree polynomial with integer coefficients that has zeros 3i and –1, wit -1 a zero of multip...

A: To find a fourth‐degree polynomial with integer coefficients that has zeros 3i and -1, -1 a zero of ...

Q: Question 4 is not smooth. Assume b=11. Find the value of a at which the plane curve traced out by th...

A: Let's find. 

Q: Use the formula for the binomial series: m(m-1)2 + 2! m(m-1).(m-k+1),k + .. (1 + x)" = 1+ mx + ... k...

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Q: Consider the integral dx . Using u-substitution, what is an appropriate u and du? 2e -2x A u=/3 e2*....

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: y' = xy+3x-y-3 xy-2x+4y-8

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Q: みm 'cU24onba buimoll ut anos Give answers occurate to o tu100yら19 SONe the foilowing tigures 6.8= .3...

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Q: 2 y+ 3 dy y + 5y + 6

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Q: Find the radius of convergence and the interval of convergence. k(k + 10) k=1 Radius of convergence:...

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 3 %3D P4(x) ...

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Q: 2x 3. Show that f(x): | V16+ t4dt has an inverse, and find (f-1)'(0).

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Q: Verify that f has an inverse function. Then use the function f and the given real number a to find (...

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Q: Score Grade/Section: Date 13. What is the solution of the inequality? A. x > -1 or x 1 or x -2

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Q: 6 - x 12. Solve the rational inequality x < 2x -5

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Q: Use polar coordinates to calculate the volume of a sphere of radius R.

A: This question is based on application of polar coordinates integration.

Q: hdefinite integral using integration by parts with the given choices of u and dv. X COs 8x dx u= x, ...

A: We will fill in the blanks with appropriate values. 

Q: Integrate the following: xdx 1. S x²-x+1 xdx 2. S V9x4-1 dx 3. S XVx-1

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Q: sec Hovy long it will tace the bor te ach 99°C I Round the ani wer to one deaimal place ] Tsec

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Q: 9)6

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Q: dX; = X;(ydX, + tdt), d Хо 3D 1.

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Q: 11. Simplify the following function by rewriting it as one fraction. (Your final simplified result s...

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Q: 4. Given the function f(r) = 3 - 6.r+2, discuss its relative maximum and minimum points, the interva...

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Q: Question The derivative of the function y = cos(xln 3) log3(sin x) is:

A: We will find the derivative. 

Q: Identify the problem whether a Permutation or Combination. Write the given of the problem and solve ...

A: Permutations and combinations

Q: x2-7 2. S dx х3-12х+16 9y+14 3. S (y-2)(y²+4) ay 4. S х3-х2+1 dx (x2+2х+2)2

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Q: Using appropriate substitution, 3 the integral J1 x(3+ln(2x))² dx is equal to: 1 1 1 1 3+ln 2 3+ln 6...

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Q: Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x [0, 4], then find the area of...

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Q: Using appropriate substitution and taking a + 0, 3tan(ax) the integral S dx is equal to: cos² (ax)

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Q: Question * Using integration by parts, the integral Sxsec(2x) tan(2x) dx is equal to:

A: The integration of the integral is xsec(2x)tan(2x).

Q: Which of the following statements is true about the function below? 6z² +8x+2 1-3r if æ # g(x) 4 if ...

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Q: If Q = 10F* – -+ F3 + 3F2, then find Q""(2).

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Q: Show that the function f(x) = 1 – I - x² is continuous on the interval [-1, 1].

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Q: Find the indefinite integral. (Use C for the constant of integration.) cos 5 t dt COS V sin t

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Q: 4xdx х2-х+1

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Q: 3. The segment joining R(2, 3) and Q(6, 7) is produced beyond R to a point Po so that Po is five tim...

A: We want to find coordiante of p

Q: B) Find the third derivative of the function: Y = + VX3 %3D

A: We have to find third derivative

Q: In a certain electronic factory, the ratio of the number of male to female worker is 2:3. If one hun...

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Q: Solve the given diffe rential equation by using an appropki ate subrh tution The DE is a bernoulli e...

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Q: 8. . cos?rsin®x dx. COS 프2

A: Product Rule of integration : ∫u.v dx = u∫vdx -∫(dudx∫v.dx)dx dsin(x)dx=cos(x)  and dcos(x)dx=-sin(x...

Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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Q: Find the fourth derivative of the function f(r) r - 32+ 2r3- ² + 4x- 10. 4. Find the first and secon...

A: find the derivative

Q: Find the indefinite integral. x2 + 8x + 5 x3 + 12x² + 15x + 6 xp

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Q: Find the nth Maclaurin polynomial for the function. 5x – 4 f(x) = n = 4 %3D x + 1 Pa(x) =

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Q: aS) A Graph the curve Y=-2x (x - 4)x + 6)(N - 2) between the value of then find the area of the fini...

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Q: Find an equation of the tangent line to the graph of the function at a given point. Note: You may/ma...

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Q: х3(1 — х)8dx

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Q: Find the indefinite integral. sin 70 Vdos ve de COS 70

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Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A: r = radius of circle a = length of each side of equilateral triangle