Direction: Evaluate the following functions. Show the step by step process by using the limit laws. Like my given examples. 1. lim () x→25 х-25

Q: 1 4. Determine the value of b and k such that f(x) = kyx – + In (x³) + bx has Vx an inflection point…

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Q: 7. Find the linear approximation to f(1) = VI at a = 27. a. Use it to approximate 27.2. b. Use a…

A: Given problem:- Find the linear approximation to f(x)=(27)(1/3) at a = 27 . a. Use it to approximate…

Q: -1 1

A: Given that cos(arcsin(-1))   we know that arcsin(-1) equal to π/2 or 3π/2

Q: If the integrand is positive the antiderivative is also positive. 9. The antiderivative of a…

A: Solve for each part and determine whether it is true or false.

Q: 1. Which of the following is a solution to the equation sin (x) + 2 = 1? 270 degrees 180 degrees 60…

A: Given problem:- Which of the following is a solution to the equation sin (x) + 2 = 1? 270 degrees…

Q: The vector v and its initial point are given. Find the terminal point. v = (4, -9); Initial point:…

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Q: a) Determine if the geometric series below is convergent or not. 8" -1 Σ n=1 7h +1 The series is…

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Q: Needed

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Q: Evaluate the definite integral: = rp |I – ,7|

A: Given: I=∫05x2-1dx   From the rule of inequality; x2-1<0 when -1<x<1x2-1>0 when x>1…

Q: Find the Maclaurin series of the function. f(x) = In (1 – 6x) %3D Choose the Maclaurin series. 6"x"…

A: f(x)=ln(1-6x)f(0)=0f'(x)=11-6x(-6)f'(x)=66x-1f'(0)=-6f''(x)=-36(6x-1)2f''(0)=-36f'''(x)=432(6x-1)3f'…

Q: | Evaluate the definite integral: 4+ 5x? dx

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Q: 4. Evaluate y = sin¬1 (x) when x = 1 %3D O 37 2 -1

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Q: The antiderivative of the function 6. + 8x is. x2 f(x) -6 + 16.0x² + c -6 4.0x? + c - 6 4.0x2 + c -…

A: Solving

Q: The function gives the cost to manufacture x items. C(x) = 25,000 + 50x + 800 ; x = 150 Find the…

A: We want to find average cost per unit of manufacturing.

Q: Let {an}-1 be a positive sequence which satisfies nan+1 1. Prove that > an converges n=1 a1 Prove…

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Q: 24 1 a) Evaluate J x-8xy+16y² dxdy=? 2

A: Given that the double integral  To find:- solve the double integral

Q: S xsin²xdx 2. х

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Q: CoSx dx sin2x-5sinх-6

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Q: Y = 4 - x2, and 2y = 4 - x2

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Q: 10. Find the average value of the function f (x) x + Vx %D on the interval xe[0,8]. Graph on Desmos.

A: Given problem:- Find the average value of the function f(x)=(1/2)x+x(1/3) on the interval xe [0,8].…

Q: х—1 dx c4 –1

A: Basic integration is done.

Q: Test the series for convergence or divergence. (-1)" + 1 2n4 n = 1 converges O diverges If the…

A: See the answer below

Q: Evaluak the following limits 9-x VX-3

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Q: find the intervals where the function is BOTH decreasing and concave up. f(x) = (x^3) - (7x^2)-5x+9

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Q: Find the limit. Use l'Hospital's Rule if it is appropriate. If there is a more elementary method,…

A: Find your answer below

Q: Ex : Express the Sum o+ 2+4+6+8 in Sigma nata tion. -2

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Q: a) Find the second and the ninety-seventh term of the sequence 8 15 22 29 ( 18' 33' 48 ' 63 the…

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Q: Q: Find the equation of the tangent plane to the surface:- z-Ln(xj) -x5J , atthe poit (7,4)

A: The given surface is z=lnx2y-xy=fx,y at the point -12, 4. The equation of tangent plane is…

Q: The value C for the solution of the initial value problem f'(x) = x4 – 8x + 4, given that f(0) = 0.…

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Q: 2. Find the dimensions of a rectangle with an area of 225 square cm, whose perimeter is as small as…

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Q: 16 – 8x f(x): x2

A: Follow the procedure given below.

Q: . A-line perpendicular to the plane 3x-4y+z=1 passes through the point A(-1,3,2). Find the…

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Q: Suppose f(-1) = 7, f'(-1) = 6, and g(x) = r*f(x). %3D The tangent line to g(r) at x = 1 is given by…

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Q: 3e" + 3x + 10 cos x + 2)dx .2

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Q: Find the following indefinite integrals. x* – 5x dx. 2. x3

A: Answer is given below.

Q: Write an equation in slope intercept form for the line 5 and a y-intercept of 9. Then. with a slope…

A: We know that the equation of line in slope intercept form is y=mx+c where m is the slope and c is…

Q: The average annual price of single-family homes in a county between 2000 and 2010 is approximated by…

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Q: y = sin* 3x – cos" 3x sec 4x y = tan 4x

A: Note:- Here your given statement is incomplete for which question you want to apply Quotient Rule…

Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

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Q: х—1 dx х4—1

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Q: The value C for the solution of the initial value problem f'(x) = x* – 8x + 4, given that f(0) = 0.…

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Q: Find the absolute maximum value of f(x) = x2 – 2x + 12 over the interval (0, 4]

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Q: 8. Which of the following is the solution to the equation sin? x+ 3sin x - 4 = 0 0° 90° + 360k 90°…

A: Given query is to find the solution of the function.

Q: evaluate the following limits (x+3)3-27 limy -20

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Answer the following True or False. Let f(x) be a continuous increasing nonnegative function. Then…

A: Let f(x) be a continuous increasing nonnegative function.Then the left endpoint Riemann sum…

Q: dx. х2 + 4 3.

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Q: Question 1 f(a)da 7 -2 3

A: The given figure is:

Q: Find the determinant of the matrix by taking the minor and cofactor of the elements in the second…

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Q: Find the limit. Use l'Hospital's Rule if it is appropriate. If there is a more elementary method,…

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Q: |(3e" + 5z" + 6 cos a + 2)dr = 3e" +a* + 6 cos a + 2r + c ez - a + cos a + 2+c 3e* + 25 + 6 sin z +…

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