1. Find for each of the following: dx d) y = e +x* +e° g) y =x2r-5 h) y = log3

Q: Direction: Translate the following notations into statements in terms of the area under the curve.…

A: LetI=∫212dxWe know that ∫abfxdx=-∫bafxdx, a<bThereforeI=-∫122dxTake constant outI=-2∫12dxWe know…

Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

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Q: The area bounded by the line y = x, the x - axis, the ordinates x =1, x = 2 is 3/2 O 5/2 O 1/2 7/2

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Q: dx kx, x(t,)=x, dt where k is a constant of proportionality, serves as a model for diverse phenomena…

A: Topic:- function

Q: The initial population of a city in the year 1998 was 128 000. The rate of change of its population…

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Q: CIT *(z + 2) dx dy dz 2. Evaluate

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Q: Evaluate the following integral. Answer in 3 significant figure, exponential form, no units, no…

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Q: जे dydy. Sec

A: To evaluate and simplify the given integral.∫sec52y dy

Q: y = e from x=0 to x=1

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Q: Find the first derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and y = ( ex – e –x ) / (ex…

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Q: 1. Find the area bounded by the curves y?=2ax, y²=4ax-a? 2. By integration, show that the area of a…

A: As you have asked multiple questions so I have answered first question as per the guidelines

Q: Convert the point from rectangular coordinates to cylindrical coordinates., (9, 3/3, -8) (r, 0, z) =

A: Cylindrical coordinate - r,θ,z where, r=x2+y2   and   θ=tan-1yx.

Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: What is the difference between a first-order linear differential equation and a second-order linear…

A: We can explain the answer as below.

Q: Find the distance from the point (3, 5, 1) to the line æ = = 0, y = 5 + 2t, z = 1+ 3t.

A: Given line x=0, y=5+2t, z=1+3t Therefore line passing through the point (0,5,1) and direction ratio…

Q: Solve the following problems. Write the correct unit and box your final answer. Topic: Applications…

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Q: A company selling widgets has found that the number of items sold z depends upon the price p at…

A: A company selling widgets has found that the number of items sold x depends upon the price p at…

Q: Homogeneou dinan Equati on Oblain the differemtial equation 1. y= 7-2x + e

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Q: 1) Solve the initial value problem. Show All Your Work. dy 2x+ sec? У(0) %3 — 5. | dx 2y

A: Let's solve diffrential equation.

Q: Adah has just bought a new motorcycle for $15 000. The value of the motorcycle depreciates over…

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Q: 7. (a) y(4) when y 2ln 30 1 (b) y() when y= %3D In 2t %3D

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Q: 1 11. lim, -2 Inx x-1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: evaluate

A: We will solve the integration

Q: 5. Find an expression for y(4) if y = e'sin t.

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Q: Discuss the symmetry of the graph of each polynomial function. 1. f(x)=2x 3. f(x)=-x' 5. f(x)=(x-3)*…

A: Given Polynomial f(x)=2x f(x)=x2+1 f(x)=-x3 f(x)=x4-x

Q: Consider the following initial-value problem. 4 f'(x) f(9) = 31 %3D Integrate the function f'(x).…

A: We have to find the function.

Q: The velocity function, in feet per second, is given for a particle moving along a straight line.…

A: Here, the velocity of the function is given as: v(t)=t2-t-182; 1≤t≤15

Q: L(e3t cos 2t)

A: We know, L{eatf(t)}= F(s-a) , where F(s)= L{f(t)} L{cosat}=s/(s²+a²)

Q: 4. Which of the following is the maximum value or the minimum value of the graph of polynomial…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: Given;  Radius=9cm dr/dt=0.4 cm/min

Q: x² cotx³ cscx³ dx =

A:

Q: How many solutions does the follow equation have. Explain e* = 0

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Q: A company produces a special new type of TV. The company has fixed costs of $486,000, and it costs…

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Q: TE THE FOLLOWING (x5- 2x3-2x)dx x²+ 10

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Q: (メ+ッ)dx + (x4ッ)dy =0 dx dy x yz x?y

A:

Q: 4. Solve the equation: (D² – 3D + 2) y = 2e* + 8 O y = cje2* + c2xe¯* + 4 + e* O y = cje2* + czeť +…

A: Explanation of the answer is as follows

Q: Find the derivative of the following function F(x) (2t – 1)' dt

A: To find the derivative of the following function.Fx=∫x2x72t-13 dt

Q: Q1: Find The Fourier series for the function defined by 0 <x < 41 -4 <x< 0J f(x) = {* - %

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Q: IV. Suppose z is a function of r and y, and tan Vy² + x² = z*e®y. Solve for dz dz and

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Q: Given the surface 9x^2 − 4z^2 = 9y. 1. Find its traces on each coordinate plane and on the planes…

A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Let's find rate of the increasing the  volume.

Q: Solution: Here * = Sin x The graph is Ine Shadded negion find i The required of we have to the area…

A: Let's find  area of given curves y=e^x from x=0 to x=1.

Q: Newton's Law of Cooling says that the temperature of a cooling substance is T = A + (T, – A)e*t, A…

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Q: 18. Convert 5 radians into degrees. First find the exact answer (no decimals or rounding, please).…

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Q: 3. Find the compound amount and interest on P1, 500 at the end of 35 years and 9 months, if the…

A: Question number 3 has been solved as per the requirement of the student.

Q: 5. (a) Let z = (a+ ai)(b+ bv3i) where a and b are positive real numbers. Without using a calculator,…

A: See the answer below

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: MULTIPLE CHOICE Question 5 Given the following matrices, find 2B- A. -20 5 3 2 0 and B = 17-3 4-3 1

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Q: dy Use Picard's method to solve dx -xy, y (0) = 1 Find y3(1)?

A: Given :dydx=-xy =f(x,y)y(0)=1

Q: 1. Evaluate (i) dy dx, 3

A: