Question 3 Evaluate the limit. Hint: Factor and enter decimal answer. x + 3 x-3 x² + 8x + 15 lim

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Q: Q-2: a) let f(x) = x^-8x² + 10. Find the intervals on which fis increasing or decreasing and find…

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Q: ¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate…

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Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Let f(x) = f'(x) = f'(9) = 4log7 (x)

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Q: Find the average value of the following function where 9 ≤ x ≤ 11: f(x) = X C 81 dx

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Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

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Q: . A rectangle has a perimeter of 6x + 9x² - 10x +5 and a length of x. Find the width of the…

A: Given: Perimeter of the rectangle is 6x3+9x2-10x+5 and length is x.we need to find the width when…

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A: given  P = x^2 y x+y=12

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Q: For the curve given by the vvf r(t) = ti + 2t²j+t³k, find the unit tangent T(t), principal normal…

A: I have appended the formula used in the solution part of the question

Q: Find the average value of the function over the given Interval. (Round your answer to three decimal…

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Q: 3. Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y)…

A: At first we derive second order partial derivative of the given function   f(x,y)=yFxy.

Q: The function f is shown below. What is the value of answer in simplest form. -10 -9 -8 -7 -6 -5 4 3…

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Q: dx b) √ COS √x cos(1-√√x) 818

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Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Q: sin(x - a) lim x→a 2(x²-a²)

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Q: 1.5: The area of the region enclosed by the graph of f(x)=√x and the x- axis on the interval [0, 4]…

A: Area bounded between the curves : Consider the curve y=f(x) and x-axis on the interval a,b , then…

Q: (a) As an iterated integral, with limits of integration A = B = C = D= Suppose f(x, y, z) = E = F=…

A: Let's evaluate triple Integral.

Q: у=ех

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Q: 5) each k=1 (- series, find the sum. k - 1 6) k=1 +1) (k+2)

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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Q: In the below series find the missing noumber  2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

A: Given data:- The below series is given, 2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

Q: Solve the following first order differential equation: dy y² +49 +3 35 4 x² + 2x³-3x² dx == 0 given…

A: Differential equation: 35x4+2x3-3x2·dydx-y2+49x3=0

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: 12- The system x' = x + 4y, y' = y + x has two eigenvectors.

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Q: (2x+5)³(52²-2x) 4. Use logarithmic differentiation to find the derivative of the function y = √2x+5

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Q: f(x) 3. What does lim = 0 show? X→∞ g(x) O g(x) grows faster than f(x) as x goes to infinity. Of(x)…

A: The given limit is limx→∞fxgx=0

Q: 5 ΣΕ j=1

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Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

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Q: 1. Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0, 1, 1).

A: Please see the below picture for detailed solution.

Q: 2 Let F(t) = (+²5¹ √5t – 2, sin (5t)). t-5' fF(t)dt f(t)dt = ([ Find (don't include the +C) + C

A: Above question is solved.

Q: Using logarithmic differentiation, find the derivative of e-3x √√2x-5 (6-524 f(x) =

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: 5 Suppose f(x) dx = 4 and g(x) dx = 3. 96 -3 -3 5 Evaluate (3 f(x) + 2 g(x)) dr. -3 Remember to…

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Q: Let a = . Find al. Check Answer

A: Given a→=<5,-1,-4>To find: a→

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Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1+ 2x² + 5y², the planes * = 5…

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Q: Evaluate the Integral using the following values. -206 [³x² dx = 260, [°x dx = 10, [° dx = 2 (22-7x…

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Q: Evaluate [/FO f(x, y, z) ds. f(x, y, z) = xy Z S: z = x² + y², 9 ≤ x² + y² ≤ 81

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Q: 5) Show that to order O(h²), the central difference formula for the partial derivative მ3u(x,t) əx3…

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