Q1\ Differentiate the following x+1 2)y = ln- x-2

Q: 2 dx 6) dx sec x csc x 7) -4tan x dx 8) -cot x dx

A: 1. ∫2sec(x)dxWe know that 1sec(x)=cos(x)=2∫cos(x)We know that ∫cos(x)=sin(x)=2sin(x)+C 2. ∫5csc…

Q: Calculate r:(t) • r2(e})] and n(t) × ra(t)] first by differentiating the product directly and then…

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Q: lim sin(9x) csc(7x)

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Q: Find the indefinite integral and check the result by differentiation. (es + sec?e) de Step 1 To find…

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Q: Verify if the following vector fields are conservative: 2y 21 a) A1 = (1+æ²+y² > I+x²+y² b) Ã, =…

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Q: (Use decimal notation. Give your answer to three decimal places.) rate: 1.2 m/s

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Q: Solve the given ODE using Laplace Transform 1. y"(t) – 6y'(t) – 2y(t) = 4 cos 2t – 4t3; y(0) = -2,…

A: Given

Q: Find the solution of the following differential equation: y'' − 2y'= x − e3x

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Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

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Q: A particle is moving with acceleration a(t) = 6t + 16. its position at time t = velocity at time t =…

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Q: Find the explicit formula of an arithmetic sequence with the given pr d = 12, and a6 = 68 %3D %3D

A: Topic:- sequence and series

Q: Find f '(x). f0) = (+4)5 f(x) f '(x)=|

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Q: Find the third derivative of the function f(x)=8x^7/2. Simplify so there are no negative or…

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Q: Let y tan(4x + 3). Find the differential dy when z = 3 and dx = 0.1 Find the differential dy when r…

A: y=tan4x+3

Q: Write the sum using sigma notation: 9+ 13 + 17 + 21 + ...+ 57 = B, where n=1 A = B =

A: Topic:- sequence and series

Q: 78 7 -1 V7x +3 dx =

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Q: Find y subject to the given conditions. y"= 12x, y"(0) = 14, y'(0) = 4, and y(0) = 4

A: To find y subject to given conditions.

Q: C(0, 1) B(1, 1) y = Vx R2 R3 y=x' A(1, 0) Referring to the figure above, find the volume generated…

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Q: c. 2x³ + 7x² + 9x- 18; x+3 d. 6x3 + 11x2- 11х-16;B 3х?-х-3 1. Use long division to find each…

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Q: dy when x = 1. dx If y = u" and u= 6x +6, find (Simplify your answer.) dx x= 1

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Q: 7. Find the derivative of In y + exy? ey sin 2x. %3D -

A: Here, the given implicit function is: ln y+exy2-ey=sin 2x...(1)

Q: Find the Maclaurin series of f(x) = 14 cos (-x). %3D What is the Maclaurin series of 14 cos (-x)? 00…

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Q: 1 dt 7+t+3t2 y =

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Q: 2. A bushfire spreads with burning area according to the following function, A(t) = 160t – 40t² (in…

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Q: Given the function f(x) = 3x – 5 and the function g(x) = 6x² + 8x + 27 determine each of the…

A: The given functions,fx=3x-5gx=6x2+8x+27

Q: The graph of f' is shown. Find the interval(s), if any, on which f decreases. 10 y =f '(x) -2 4 6. 8…

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Q: 2. Use synthetic division to divide the first polynomial by the second. а. х? +x-33B х-1 b. 4x -Зx2…

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Q: 0Graph the following tu Pune

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Q: Find the slope of the tangent line to the curve 4x + lay- ly = 88 at the point (3, - 4).

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Q: 2000 A television camera at ground level is 2000 feet away from the launching pad of a space rocket…

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Q: Evaluate the integral. 1/3 6 sec x dx 0. n/3 2 6 sec x dx %3D 0.

A: To find out the integration.

Q: 3. Find two elevation angles that will enable a shell, fired from ground level with a muzzle speed…

A: Solution: here we use the range formula

Q: ii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows:…

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Q: xdy + (y – cos x)dx = 0, y() = 0 0, У 8. Solve the IVP:

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Q: Find all critical points of f(x) = 1 + 8x – x² and use the First Derivative Test to determine…

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Q: Find the exact value of the logarithmic expression without using a calculator. (If not possible,…

A: We have to find out the value

Q: lim (4x - V16х? + 3х — 5 -Зх — 5 x00

A: Given :

Q: 4.) Evaluate: xe* dx

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

Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: 021 - In simpson's 1/3rule the intervals must be c) non of them [2 3 022- The eigin value of matrix…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 1 dx x (1+x4)4

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Q: 4. 7 (t) = (4t, –2t, /5 t) = (4t, -21, v5 ') %3D

A: This is a problem related to vector differentiation. Based on the general formula we can calculate…

Q: solve

A: We will solve the problems.

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 - 3t) %3D Find the…

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Q: ab³/2 (7) If x = then log(x) = c2d' %3D (A) log(a) + log(b) - 2log(c) - log(d) (B) log(a) + log(b) -…

A: Given problem:-

Q: Ing light is located 10 feet from a wall. The light completes one rotation every 3 seconds. Find the…

A: From the given data: Here, the complete 2π rotation is done in 3 seconds.  So, dθdt=2π3 rad/sec

Q: Perform a first derivative test on the function f(x) = x/25 - x;(-5,5]. a. Locate the critical…

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Q: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the…

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Q: 5 5 5 The functions f and g are integrable and f(x)dx = 7, g(x)dx = 4, and f(x)dx =2. Evaluate the…

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Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x* 1 g(x) 7x + 1 (Express numbers in…

A: Given problem:-