Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t < 6. 2ryz da + x²z dy + x²ydz=

Q: Evaluate the limit 25 — b lim b→25 5 – vb

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Q: General solution of x dy = (2xex – y + 6x2) dx %3D

A: The given equation is: x dy=(2xex-y+6x2)dx That can be written as:…

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Q: D. Define the multiplication operation * as modulo 10 in G = {1, 3, 5, 7,}. Cr table for this.…

A: Topic:- algebra

Q: Evaluate the given integrals. 1. ſ cos v2x dx 2. fx a*dx

A: Please see the answer below.

Q: 6. Evaluate the following: (ey)dy dx 0. A. e-1 e-1 C. 2e +7 2. D. e?

A: Given: I=∫01∫0y3exydydx   As we know the basic integral formula; ∫eax+bdx=1aeax+b+C

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A: y=(x – 1)(2x – x2)   +sin-1(x – 1) y'(x)=d(x – 1)2x – x2   +sin-1(x – 1)dx        =d(x – 1)2x – x2…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 3 and x = 1 x intercepts…

A: We have to find the function

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Q: dx V(z – 2)° – 11 Vxt-2)* - || x - 2 du 1 (steps) da = /11 du: V1I u = x-2 du = dx Substitute u =…

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Q: Evaluate the limit, using L'Hôpital's Rule If necessary. (If you need to use co or -, enter INFINITY…

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Q: Find the first partial derivative wx, wy, wz of ( x  +  yw )2 –  ez  – 2 = 0

A: Let's find partial derivative of given function.

Q: Converting 1530 degrees to radians will correspond to which value? 19n 3 201 B 3 29Tt

A: The value of θ° to radians is given by        ∅ = θ×π180  radians

Q: Find the volume of solid generated by revolving te area enclosed by : x=y²+1, x=0,y=0 and y=2 about:

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Q: Evaluate the definite integral. es dx x/ln x v 5 6568542194924

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Q: даду

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Q: 17. If you knowf (0) = 625 and f(4) = 16 then: (a) Find a formula for f(x) assuming that it is…

A: In this question, we want to find a linear function f(x) which satisfy the given conditions.

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A: Let's find ratio of given complex numbers.

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A: Here we have to choose the corect option.

Q: B. Directions: Compute the definite integral of the following functions using the Substitution Rule.…

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Q: What is the exact value of csc(– 1305°)? V3 A B D 2.

A: using csc(-x)=-csc(x) and  csc(360n+x)=csc(x)

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Q: sec =zydy

A: Given

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A: Let's find volume of slice of pizza.

Q: x² + 4x + 1 · dx | (x – 1)(x + )(x + 3)' 3 국lnlx-11+ anlx +11-x + 31 +C Inx - 1| + Inx + 1| + Inx +…

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Q: Question 3. Find f/(x). If f(x) = tan-1x?

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Q: Convert to a rectangular coon 12. (3,*)

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Q: Find the sum: - 4+ – 5+ – 6 + ... + – 17 | Answer:

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Q: Use TRIGONOMETRIC SUBSTITUTION 1 to find f dm m²V9-m2

A: LetI=∫1m29-m2dmI=∫1m232-m2dmSubstitute m=3sin(x)Differentiate…

Q: 12. Solve 2cos²(20) = 1. List the solutions that are: 0 < 0 <n %3D

A: Here, the given equation is: 2cos2(2θ)=1⇒cos2(2θ)=12⇒cos(2θ)=12 or cos(2θ)=-12

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, C = 6 (x – 6)²…

A: We have to find out the polynomial

Q: 11. Given the functions: g(x) =In(4 – x) and h(x) = 4 – x² find and simplify the following: (a) h(x…

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Q: y = sinx from x=0 to x=n

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Q: Evaluate the limit, using L'Hôpital's Rule If necessary. (If you need to use m or-m, enter INFINITY…

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Q: What is the range of the inverse sine function y= sin- (x)? (-골, 글) A 2 2 B ( 0, π) 2'2 D [0, 1]

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Q: Find the derivative of the function. y = x2(8x2 - 9x) y' =

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Q: 6. S (10 x - 40) dx x 2 - 8 x + 15 8. S (e 5x - e 2x + 8) dx 2 e 5x 7. S 10 cot 2x dx

A: We have to find the integral.

Q: Consider the following limt. lim - (x + 5) Find the Iimit L. (a) Find 8 > O such that |fx) - L| O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use Partial Fractions x* + 3x? – x – 8 dx x3 + 4x

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Q: 8 What is the range of y=4sin A [-2,6] B [-6, -2] © [-6, 2] D [2, 6]

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Q: Consider the following initial-value problem. f'(x) = 6x2 – 8x, f(3) = 21 Integrate the function…

A: Given: f'x=6x2-8x, f3=21   As we know the Power rule: ∫xndx=xn+1n+1+C

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A: Topic:- trigonometry

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Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hopital's Rule. sin(9x) lim 7x…

A: We have to find the limit

Q: 14. Re-write the equation f (x) = x² – 10x + 16 in vertex form. Note: the author of your textbook…

A: Given:      fx=x2-10x+16   Set the polynomial equal to y to find the properties of parabola.…