y=x 2 y = x+1

Q: xdx 41. 12-х

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

Q: Find the conservative vector field for the potential function by finding its gradient. g(r, y, :) +

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Q: Condense the expression to the logarithm of a single quantity. [9 In(x + 4) + In(x) – In(xº – 8)]

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Q: C- prove that 1-+-- Find Maclaurin series of tan-(x). Hence

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Q: Find V. (V x F) if F(x, y, z) = 4 sin xi + 7 cos(8x – 9y)j+ 9zk. V·(V × F)

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Q: Colleen's office equipment is depreciating at a rate of 9% per year. She paid $24,500 for it in…

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Q: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) arcos…

A: Givencos-1cos-3π2We know…

Q: Find the volume between the cone y = Vx² + z² and the sphere x2 + y² + z² = 25. volume =

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Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: Find V x (V × F) if F(x,y, z) = 8xyj+ 4xyz k. V × (V × F)

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Q: S(1 + tanx)² dx

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Q: Solve tan(x)=5in the interval osxs360°,giving your solutions to 2 decimal places

A: Given,  tanx=5 x=tan-15 x=78.69°

Q: Suppose a certain baseball diamond is a square 90 feet on a side. The pitching rubber is located…

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Q: Q1) Determine if the following integrals converge or diverge. If the integral converges determine…

A: Given problem:-

Q: x + 2y = 1 , x – 2y = 8 . Credit will be given for use of the method, and not for the so y =-7/4.

A: We will solve using cramers rule.

Q: X+3 Q4) Find the integration by using: J: dx 2x3-8X

A: This question is based on indefinite integral.

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 13 9ts r(t) = e"i+etj K(t) :

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Q: 8. Evaluate the double integral ry=2x L3) dydz. x=1

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Q: 11. Rules of Definite Integrals: If f(x)dx =12, S" S(x)dx = 6, and "S(x)dx= 4 , find the following:…

A: We need to perform integral.

Q: Find div F and curl F if F(x, y, z) = x*i – 11j + yzk. div F= curl F=

A: Vector

Q: dy cos (x) cos (Y) %3D da O a. 2 In sec (3) +tan (3)| = %3D O b. 4 In sec (3)) + tan (y) %3D

A: Given: dydx=cos2x cosy

Q: Find V. (V × F), if F(x, y, z) = 3e²*i+9xe*j – 4ev*k V· (V × F) =|

A: Use the curl and divergence for the F.

Q: 15 of 20 -722 –8x =? limz→00 3–72²+6x+6 O Does not exist O 00 O 7

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Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

Q: What is the instantaneous slope of y == at z = 5?

A: for the instantaneous  slope for a function f(x) at x=a we have to find f'(x) and then put x=a in…

Q: Find V x (V x F) if F(x, y, z) = 2:xyj+ 9xyz k. V × (V × F) %|

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Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x? N(x, y) = x² - 2y (I): (2xy – 3x )dx…

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Q: detailed computation in determining the height of the cabin or part of the Ferris wheel at a given…

A: We are given a ferris wheel with the following informational : diameter : 64 m No of cabins : 32…

Q: In a

A: We have to find given indefinite integral.

Q: Find the second order Taylor expansion of [15] f(x,y) = (1 +4x2 +y2)1/2 about the point (1,2) and…

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Q: Find div F and curl F if F(x, Y, z) = 11y°z°i – 3x*z°j – 6xy°k. - div F= curl F=

A: The given vector function is: F(x,y,z)=11y6z5i-3x4z6j-6xy3k Let, F(x,y,z)=F1i+F2j+F3k then…

Q: 1. 5x²+4x2-5 dx

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Q: Question 5 Consider the exact first order diff. equ: M(x, y) = 2.xy –3x? N(x, y) = x² - 2y (I):…

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Q: Given a differential equation dx with the initial condition, y cos (2x) 8

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Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: Describe the graph of the equation. r = 14 sin 17t i – 14 cos 17t j O It is a circle of radius 14 in…

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Q: Problem No. 1: Evaluate - dx using basic substitution method.

A: First I have used the substitution to make integral easy and then evaluate it.

Q: Example 22 Find the eccentricity and directrices of the hyperbola given x? y? 1 9 16 Sketch the…

A: Given: x29-y216=1

Q: Integration

A: We will solve the integral.

Q: In x

A: A detailed solution is given below

Q: D. Find the orthogonal trajectory f the family of curves y= x+h %3D

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Q: Find r'(t). r(t) = (tan-'(5t))i+t cos(t)j – Vik NOTE: Enter your answer in terms of i, j, and k.

A: r(t)=tan-1(5t) i+t cost j -t kddt tan-1(5t)= 11+(5t)2 ddt(5t)ddt tan-1(5t)= 51+25t2 ddtt cost=cost-t…

Q: A pencil cup with a capacity of 36 in.3 is to be constructed in the shape of a rectangular box with…

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Q: 4. Consider the matrix А 5 2 One of the eigenvectors of A is given by [1 -1]'. Find the eigenvalues…

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Q: 2. Find the r educed echelon form of the fo A = 0 0 0 6 54 0 (714161 Show your working

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Q: 10 dx 5. S (10 +1)5 6. S 2r(e**+1 – 2**) dx

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Q: 2- Sinx-y cos?x =.

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Q: e i+ - 1 (P-1)i-(e1-1)j+글 i - k

A: Given query is to find the integral.

Q: C. Find the general solution of the given variable separable equation. 1. 2cosx cosy dx - 3Isin x…

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Q: Find V x (V × F) if F(x,y, z) = 8xyj+ 4xyz k. V × (V × F) = (4(y+2), 4:x, 0)

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