A) Find the first five partial sums of the given two series and determine whether they appear to be convergent or divergent. If you find that a given series is convergent find its approximate sum 1+1/8+1/27+1/64+1/125+…

Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: Find the area bounded by y = 4x -x^2 and x = 0, and y = 4 using two methods (vertical and horizontal…

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Q: Use the method of undetermined coefficients to solve the initial value problem. 33 y ==cos2t 10 33…

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Q: Use trigonometric substitution to find or evaluate the integral. (Use C for the constant of…

A: To use trigonometric substitution to evaluate the integral. ∫x38+x2dx

Q: Find if y = dy dx dy dx 5x+2 10x6 C

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Q: A police car is located 40 feet to the side of a straight road. A red car is driving along the road…

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Q: Let f: [1,1]→ R be a function given by f(x)=2x-x2. Then the inverse image (preimage) of [0,4] under…

A: The answer is option D

Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of 8,…

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Q: 1 . Find the arc length for y = √√2-x² for 0 ≤ x ≤ √√2. Check your answer by noting that the curve…

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Q: Question 32 Find the average rate of change for the function) f(x) = x² + 7x from 1 to 4. 12 desmos…

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Q: Given that lim f(x) = 4 and lim g(x) = -2. Find the value of x-2 x-2 lim 4f(x) + x-2 [g(x)]³ ) 2

A: we find the value of given limit

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Apply Green's Theorem to evaluate the integral (-5y² dx-5x² dy), where C is the triangle bounded by…

A: greens theorem

Q: Let f(x) (1) (ƒ + g)(x) = = - 9x + 8, g(x) = x - 1, find the following: (2) (ƒ − g)(x) = - (4) (3)…

A: To find the value of given function and their domains.

Q: Find the area of the given region. y = sin(x) R|C I

A: We are asked to find the area of the region

Q: Region R is bounded by the graphs of C₁ : x = y + 1 and C₂: x = 3 - y² as shown in the graph below.…

A: Given: Region R is  bounded by the graph x=y+1 and x=3-y2 as shown in question. USE: cylinders…

Q: 3( Determine whether or not the improper integral is convergent, and find its exact value if it is…

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Q: Determine the area of the shaded region in the following figure. The area of the shaded region is…

A: We have to find area

Q: = [₁ rx Let I= f(x) dx, where fis the function whose graph is shown. y 12 8 4 1 2 (a) Use the graph…

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Q: dy 5 Find dx 2 tan (x-Y) = 6+x²

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Q: Find lim lim h-0 h→0 f(6+h)-f(6) h f(6+h)-f(6) h if f(x)=x² +4. (Simplify your answer.)

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Q: Evaluate the following integral: sin²(a) da

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Q: Given f (x) = 4x²-3x + 2. The slope of the normal line to this curve at the point (1,3) is O-5 5…

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Q: = f(1) dt, where f is the function whose graph is shown below. What is the value of g′ (-2)? Let…

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Q: Find the derivative of the following function given

A: Our Aim is to find the derivative of the functions given below:-y=sec2 (x)-tan2 (x)  -(i)

Q: Letf(x) = x² – 5x + 6, g(x) = 5x – 1, find the following: (1)(f + g)(x) = (2) (ƒ − g)(x) = - (3) (ƒ…

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Q: π/2 √1-cos2xdx

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Q: For the given functions f(x) = − 9x², g(x) (1) (fog)(x) = (2) (gof)(x) = (3) (ƒ ○ ƒ)(x) = (4)…

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Q: sin a Given: f(x) 2x ' k, { if x #0 if x = 0 What should be the value of k so that f is continuous…

A: This question can be solved using the concept of continuity of a function at a given point.

Q: For the function shown below, find (if the quantity exists) (A) lim f(x), (B) lim f(x), (C) lim…

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Q: Find the general solution of the following differential equation. 121y" – 4y = 0 NOTE: Use c₁ and c₂…

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Q: What is lim O -∞ 0 1 2 O +∞ x^x + x^ I 2-700x + √x-2x√x²

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Q: Find h'(t) if h(t)= h'(t)= 3 1/2 3 3/5

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Q: x² + x + 72

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Q: (iii) Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

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Q: 4. Graph the equation: f(x): = 1, -2x + 4, -2, -3≤x≤0 0 ≤ x ≤ 3. x > 3 -1 5+ 44 3- 2+ +1 -1- -24 -3-…

A: This is a graph of piece wise function

Q: Determine whether the series DIVERGES.) 6-77 14" 00 Σ n=1 n=1 6-77 14" 123 Tutorial converges or…

A: Let's find series diverges or converges.

Q: A car sharing service offers a membership plan with a $40 per month fee that includes 10 hours of…

A: A car sharing service offers a membership plan with a $40 per month fee that includes 10 hours of…

Q: Find the value of the limit lim 01 0 0 O DNE x3 x+0 x³ + x2 < Previous

A: On solving this we will get

Q: Please help me understand and the steps taken in the process. Thank you Given Find the following. a)…

A: Given: fx,y=x3y2-3xyWe need to find a) fxb) fy

Q: Find each limit. Use oo or ∞o when appropriate. 2x - 10 (x-10)² (A) lim f(x) X-10 f(x) = (B) lim…

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Q: ve the given init value problem. dy dx 3x²y + y² 2x³ + 3xy' y(2) = -3

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Q: the answer is 3+6N but i dont know why, so please go step by step/explain how you get that answer.

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Q: A car sharing service offers a membership plan with a $40 per month fee that includes 10 hours of…

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Q: Evaluate f √x² - 16 8 -dx

A: use the substitution method for solving the integral.

Q: The piecewise function f(x) is graphed below. Use the graph to find the average value of the…

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Q: Suppose that a sequence {an} is defined by the equations 1 = Which of the following is true about…

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Q: olve the given differential equation. All solutions should be found. dy x - 2y dx X

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