Question 3. Find the general antiderivatives of the following functions. 1. f(t) 23 6 1 2. g) 3. r(e)-5+cos

Q: 13. What is 2sinx cos x dx? TRONG A. +C In 2 C. 2 cos.x B. +C 2sinx In 2 D. In 2 14. Which of the…

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Q: 2. Which of the following functions is of exponential order? * 4 f(t)= Sin 4t f(t)= 5{VT + A.) O B.)…

A: The function of exponential order is determined as shown below.

Q: QUESTION 5 Given thatf(x) = 2 if x changes from 1 to 1.05, estimate the value off(1.05)using 2+ x2 .…

A: Given that: f(x)=22+x2

Q: 1 g(x, y) = = cos (Tx/y) + %3D log3 (x – y)" Do as indicated. 1. Determine dydx

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

Q: a) L 8(t) cos(48tt) dt b) 8(t – 5) cos(nt) dt c) L[8(t +3) – 28(4t)]dt

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Q: I. Evaluate the following function below. 3 2 1. S sin'y ( 2 – 3 cos y )´dy 9 3. S sin'x dx 9 4. J…

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Q: many

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Q: 7. If f(x,y) = y³ loge x³ + x² sin y – y? cos x, find (i) fx (ii) fxx (iii) fry (iv) fy (v) fyx

A: we find the partial derivative of all parst. see 2nd and 3rd step.

Q: 1. Find the antiderivative of each of the following functions. 3 a. f(x) =+ e* + Vx b. f(x) = sin…

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: Question 3 of 12 Find the general antiderivative of f(x) = 4 cos (x) - 7 sin (x) and check the…

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Q: Question 12 If L{f (t) }= | e-(s+1)! ¡2sin²4 dt_then what is f (t)? ,- (s+1)! ¿2sin²t dt, then what…

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Q: -) Prove that the given function is The general solution of the given equation a) k'y"+Ky'+y =o y=G…

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Q: Find an antiderivative of the given function. 7 cos 2x

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Q: Question 4: Consider the initial value problem aj + by + cy = f(t), y(0) = yo, (0) = y%, t> 0.…

A: Consider the given initial value problem.

Q: 1. Find -for each of the following: dx e) y =x* Inx f) In(x + y) = e*=y g) y = x2r-5

A: Here we have to find dy/dx .

Q: Question 5 x² – 25 The antiderivative of - dx is x2 – 25 – sec-lx+ C. True F False

A: ∫x2-25xdx

Q: Find the most general antiderivative of the function.

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Q: 2. In each of the following, find fyzz, fæyæ, fryz. 2. f(x, y, z) = ln(xyz) + z² tan-'(e=")

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Q: 1. Find the following antiderivatives: (b) (cos(5e) - sin(21)) dt eat (c) -2t dt 2

A: As per guideline we have to solve only three

Q: Question 1. Find the linearization of the function y = f(x) = x² sin(x) at a = T/4 and use it to…

A: Linearisation of f(X) at a is given by-  L(X) = f(a) + f'(a)(x-a)

Q: IV. Suppose z is a function of r and y, and tan Vy² + x² 2e&y¸ Solve for az az and dy

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Q 5: (a) Assume that after w months, butterflies' populace in 1000 is calculated as: f(w): = 12w +…

A: Assume that after w months, butterflies populace in 1000 is calculated as follows:…

Q: 10u +4 /ũ Find the most general antiderivative of f(u)

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Q: er the questions below: I z²,e²,4x³z + ye² COS Z > done by F in moving a particle along the cur π Ả…

A: We have to find the following conditions according to the given information

Q: QUESTION 5 The approximation of x e*dx by Simpson's Rule is 0.160602 O 0.160603 O 0.162402 O None of…

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Q: -) sin A = d.) cos M = 34 25 hy 16 24 30 K e.) sin L = f.) tan G = M. 7. K 8. 15

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

Q: 4.) (w° + wx²- x ) dw t ( x° t w? x - w) dx = 0 ( 2x +y cos xy) dx t x cos xydy COS X

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Q: s – a L{et cos bt} (s – a)² + b² * EXAMPLE 3! L{t³ + 5t – 2} = L{t³} + 5L{t} – 2L{1} +5- 1 2- - S…

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Q: d g(r)= 3re³ %3D e y= e² – e-z 5 f. 8- 3+ el

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Q: QUESTION 7 Find the most general antiderivative. Stosecx) dx (-6 O-6 tan x-C O-6 cot x -C (1 tan x.…

A: We have to integrate

Q: Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii)…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: EXAMPLE 1 Find an antiderivative for each of the following functions. (a) f(x) = 2x (b) g(x) (c)…

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Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d.…

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Q: 2. If you know (1 – a.0 s a s 1 * f(x) cos ax dx = 0 ,a>1 Find the value f(x)!

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Q: Question 7 OT 15, Step Correct Consider the function y 3x + 5x2 + 4x - 2. Find the differential for…

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Q: |(1) Solve the following D. E's :- a) Y=l+a0lY, b) y'= xy/2, c) xy'= y+Y, d) Y= (x²+ y²)/xY, e) y'+…

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Q: Question 9 Given f = xy² In (3y + 2x) + (xy)e* (ry), find dy

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Q: 1 Q22. If y=tan' x+ tan dy - then -is: dx (d) T 2 (a) 0 (b) 1 (9 (p) 1+x

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Q: 8 If y' = x In a and y(e) = 4+ e, which of the following would be the constant of integration of the…

A: Given : y'=8xlnx and ye=4+e Let us solve the given differential equation ,…

Q: 3 a) given y: (1-2n) find dy and d'y hence, evaluate dn yl)+x( ) where X =1

A: The function is y = (1-2x)3 and x = 1. Evaluate dy/dx as follows.

Q: 1. Suppose that the rate of gasoline consumption in the United States (in billions of gallons per…

A: We shall answer first three subparts as per the guidelines. You can post it again by mentioning…

Q: 4. The function g(t) = (8t)' – cosh² t + sinh t satisfies g'(c) = 0 for which value of c? (a) c= 0…

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Q: Part 2 of 2 After finding the differential dy. y= (x+4)/(x-4) Evaluate dy for the given values of…

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Q: Question 21 Find the antiderivative of f 5sin x* In 5 cos x dx. A.) 5cosx + C В.) 5sinx + C C.)…

A: To find:- ∫ 5sin(x) ln(5) cos(x) dx

Q: 7) The function (h) is.dsfined by: h(t) = 0 if t e] – 00; –1,5n[ ; h(t) = cos(0,5t – 0,25 n) if te…

A: Given :  ht=0, t∈-∞, -1.5πcos0.5t-0.25π, t∈-1.5π, 2.5π0, t∈2.5π, ∞

Q: (x – 4)e dx satisfying the initial condition y(4) = In(4). ソ= Your answer should be a function of x.

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Q: 0 1 Q3:Evaluate the irtegals [(x+ y+1)dxdy -1-1

A: The detailed solution is as follows below:

Q: QUESTION 3 For the IVP dy =x(x+y), y(2) = 2, by Euler's method y(2.5) = dx %3D 04 0 8 o None of…

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Q: Evaluate L{e (cosht – sinh nt)} 3r S+3 A. (s+3)*-n² (s+3)-a² S-3 B. (s -3)- (s-3) 2. s+3 C. (s+3) +*…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.