Solve CO (z-2)² 3ln 2-2-¹³ +C In | x − 2 − ₂ + C None of the Above 2 ln | x − 2 + + C

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A: Topic:- application of derivatives

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Q: -) Consider the sequence 1, - Determine tg- 128 2187 64 b) 79 33-80 27' 128 2187 64 79

A: Above question is solved.

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Q: 5- The tail of vectors a and b form two sides of a parallelogram. Vectors is 30 degrees, and the…

A: Area of a parallelogram when two sides of the parallelogram are given by the vector a→ and b→ is…

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Q: Find curl F if F(x,y,z) = 7exy i-8 cosy j +5 sin²z k. curl F = -7xexy k curl F = -7xexy i curl F =…

A: In this question, we want to find the curl of given vector function.

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A: The linearization of a function f(x,y) at (x0,y0) isL(x,y)=fx(x0, y0) (x−x0)+fy(x0, y0)…

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Q: Making a suitable change of variable and modifying accordingly the limits of integration, calculate…

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Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

Q: 3 10 [1] Restart Rock Co. determines that the marginal cost, C', of producing the xth climing…

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Q: X x² - a² dx

A: To find the value of given integral.

Q: 0 Determine which of the following are singular value decompositons for A = 3 VIS √13 1. |69| 0 3 13…

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Q: Find the area of the shaded region. y=2x2+x-6 y=x2-4 W

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Q: t² +3t t--3t²-t-12 b. lim (-3)²-9 u-0 น (x+h)³-x³ C. lim h→0 h a. lim

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Determine the absolute extrema of the given function on the specified interval. 1. f'(x) = 3x² + 4x…

A: Given :  F'(x) = 3x^2+4x-11 = g(x)

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A: Graph of the function is given, we have to find its asymptotes and domain

Q: What function will you differentiate to get each function? 1. f(x) = 4x³ - 6x² - 10x + 1

A: Given function, f(x)=4x3-6x2-10x+1 Aim: To find  a such  function , whose derivative is f(x),…

Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed b y=x,…

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Q: What function will you differentiate to get each function? 2. f(x) = 8x74x³ + 2x - 3 →

A: solution:-f(x)=8x7-4x3+2x-3antiderivative of f(x)F(x)=∫f(x)dx       =∫8x7-4x3+2x-3dx…

Q: 6) Use double integral to find the volume of the solid bounded above by the paraboloid 9x² + y²,…

A: We can find the volume of the solid by using double integral .

Q: 5- Determine the value for x such that the points A(-1,3,4),B(-2,3,-1), and c(-5,6,x) all line on a…

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Q: Can someone convert the final answer to integer or decimal?

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Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the…

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Q: Problem 3 Solve d² +3 d +3dy - 4y dx² dx = x²

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Q: Evaluate the line integral, where C is the giv z² dx + x² dy + y² dz, C is the C

A: See the details solution in below

Q: How much work is required to pump all the water over the top of a full cylindrical tank that is 2 m…

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Q: Find the volume of: the area bounded by the curve y2 = 9x and the line x = 4 revolved about x = 4.

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Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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Q: The point x = 0 is a regular singular point of the differential equation x²y" − x(x+3)y' + (x+3)y=0.…

A: The given differential equation is x2y''-x(x+3)y'+(x+3)y=0…

Q: kx +5 for x ≤ 2 Let fx = = x-1 for x > 2 Find the value of k for which f(x) is continuous at x=2.…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √ 1 + ex,…

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Q: Additional Activities What function will you differentiate to get each function? 2. f(x) = 8x74x³ +…

A: Let differentiation of F(x) leads to the function f(x)=8x7-4x3+2x-3 So, F'(x)=f(x)=8x7-4x3+2x-3

Q: 2. Find the sum of all rectangles shown in figure below in terms of x and y. X x/2 x/4 y/4 y/2

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Q: 1) (y ²-1) dx - 2y (²+x) dy 2) y² = x €²9-x² =C

A: See the details solution in below

Q: [₁ In(x² + 4)dx

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Q: 2. A cylindrical tank of radius 20 feet is being filled with water at the rate of 600 cubic feet per…

A: Given that,  Radius of cylindrical tank= 20 feet Water is filled at a rate of 600 cubic feet per…

Q: s) Calculate the indefinite integral using Trigonometric Substitution. X [ dx +x²

A: This is a problem related to integral. Based on the trigonometric substitution we will answer the…

Q: A circle with radius 4 units and a central angle of 110° is shown below. 4 a 110 2. The arc length,…

A: We can find the arc length as below.

Q: A manufacturer of canned food packages the product in cylindrical tin cans. The volume of each can…

A: Given

Q: What is the sum of the infinite series 1 "n=1 102m ?

A: Sum of the infinite geometric series , S =a1-r ; where , a-first term and r<1 is common ratio .

Q: Algebraically prove the identity, Left Side sin +1 1 sin 8-1 2 sec² 0. Right Side

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Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

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Q: b. lim a-1 ²ln(1-x) X -dx

A: Given

Q: Use the table of integrals to evaluate the integral. (Remember to use absolute values where…

A: ∫3 sec5(x) dx=3∫sec5(x) dxApply reduction formula: ∫secn(x) dx=n-2n-1∫secn-2(x) dx+secn-2(x)…