EXERCISE 1 df af. In each of the following, find Əx and (k) f(x, y) = /Ty + VT+ VJ

Q: Given the graph below, which of the following statements is TRUE? I. lim (sin z) = 1 II. lim (sin z)...

A: NOTE: Refresh your page if you can't see any equations. . as we can see, the function is continuous ...

Q: x3 + 8 dx

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Q: Estimate the area under the graph 1 of f(x) = from a = 5 to x2 +1 b = 13 by using n = 4 rectangles o...

A: The given function,   f(x)=11+x2 from a=5 to b=13 by using n=4 rectangles

Q: Q3. Find out values of a, b, c for which curl of vector V is zero, where V = (2xy+ 3 yz) i +(x² + ax...

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Q: f(x) = x2 + 7x +  5 x f '(x) =

A: Given query is to find derivative of the expression.

Q: dy if tan (xy + y) = dx = x. %3D Use implicit differentiation to find dy dx

A: We know,  d/dx (tann x) = ntann-1 x.sec2x d/dx(y2) =2ydy/dx by Implicit Differentiation. 

Q: Apply integration by parts: / udv = uv – - S vdu = UV sin2x – cos2x dx sin2x + cos2x

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Q: The Carteslan coordinates of a point are given. (a) (-2, 2) (1) Find polar coordinates (r, 0) of the...

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Q: Consider the region bounded by the graphs of y=In x, x=1, and y=1. Which of the following integrals ...

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Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x, y, z) = 2x + 2y...

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Q: The angle between the two vectors 1= (-9, –4, 7) and v = (36, 16, -28) is Select one: True False

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. ...

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Q: 2x +3x-2 (i) lim 2х-1 1 +1 1) lim x+2 x+3 x-3

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select o...

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Q: У(xtanx + Inу)dx + tanxdy 3D C

A: The given equation is; y(tan x+ln x)dx+tan xdy=0

Q: For the following function, find appropriate function g(x) of fixed point method: f (x) = xe* – 1 -

A: g(x)=

Q: 7 1 dv = -7 V

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Q: A community had an initial population of 6000 people in 1990.  Now assume that the population decrea...

A: topic- exponential function

Q: Find the directional derivative of the function at P in the direction of v. f(x,y) = xy P(0,-2) v = ...

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Q: 3t 3 dt +C 3lna A) True B) False

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Q: Calculate the definite integral. 4xy Vx2 + y2 dy Calculate the iterated integral. (1 (1

A: Here we have to calculate ∫014xyx2+y2dy

Q: Differentiate the functions. a) f(x) = 1 – 6x +x7 b) f(x) = (x³ + 3)² %3D

A: a)f(x)=1-6x+27x7Differentiate with respect to x   f'(x)=-6+(27×7x6)  f'(x)=-6+2x6Derivative of f(x)=...

Q: Find the derivative of the given. f(x)= cos x cot x let g= cos x and h= cot x. Then, g'= -sin x an...

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Q: Use Newton's method and find an approximation for the root of the following function accurate to wit...

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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Q: Approximate the integral to three decimal places using the indicated rule. c0.8 311 01 dx; Simpson's...

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Q: Consider tne following. (a) Set up an integral for the volume a solid torus (the donut-shaped solid ...

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Q: The equation -x2 - y² = – 2 represents a Cylinder in R3. Select one: O True O False

A: We have to tell true or false  The equation  - x2 - y2 = -2 represents a cylinder in R3  

Q: 3. %3D x +4 Start Över

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Q: Sketch the graph of the given function. Check your sketch using technology. g(t) = (a) Indicate the ...

A: ?As per our company guidelines we are supposed to answer only one question at time or moreover 3 sub...

Q: Determine if the given function is continuous at 3. * ( x + 7 |x – 2| f(x) = { x? – 2x x 3 9x 2х — 3

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Q: et kdt k A True B) False

A: First we solve L.H.S then solve R.H.S . We use the formula integration of eat=eat/a

Q: Question 3. Let P be the collection of all polynomials of finite degree. Let I : P → P be the integr...

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Q: 1. f(x) = 9-6x 2. g(x)= a. f(-1) a. g(2) b. f(1) b. f(a+b) c. f(3 + x) c. g(2 -x)

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: The revenue function Rin terms of the number of units sold, a, is given as R= 250z – 0.32? where Ris...

A: topic - functions and application of derivatives

Q: Given the differential equation y" + 7y' + 12y = 8x e-3x Determine the General Particular Solution f...

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Q: Set up an integral for the area of the shaded region. Evaluate the integral ta find the area of the ...

A: Integration of shaded area

Q: 4. Let F be a smooth vector field. Show that the flux of F leaving an infinitesimal cube of volume d...

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Q: Čonsider the following nonlinear programming problem Maximize Z = 36x, +9x¡ – 6x¡ + 36x, – 3x X, +x,...

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Q: Which of the following limit theorem used for transcendental functions is wrong? 1 O lim COS T | O l...

A: topic - limits

Q: graphing calculator is recommended. Find the following, correct to two decimal places. (Enter your a...

A: Given query is to find the the interval where function is increasing and decreasing , and find its r...

Q: Evaluate the integral. tan(10 x) sec*(10 x) dx +C

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Q: Expand $it) in Fourier series in the interva) (- 2, 2) when fit) = -2st <o %3D 1.

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Q: Apply integration by parts: S udv - S vdu = uV sin2x – cos2x dx sin2x + cos2x

A: Integrate the function (sin2x-cos2x)/(sin2x+cos2x) w.r.t. x 

Q: Given the differential equation у" — у' — 12у %3D 7ез^ cos(x) Determine the Wronskian for the differ...

A: Solving wronskian

Q: Given the differential equation ap - 2y = 15 dx Find the General Solution to the Differential Equati...

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Q: c) Evaluate [| 4xy where D is the portion of x + y = 2 in the 1* quadrant.

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Q: e(2e" – 1)dx 6x 3x A 2e - 1 B 2e 6i – e 3u © (e"-2)+ (e" + 1)4 E F None

A: This is a problem of integration. First here we will assume e^3x = t and then we will use general fo...

Q: Suppose x E Rand let A 11 x 1 x x x x x (a) Compute det A as a function of x. How does the rank of A...

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Q: 15-28 Sketch the graph off by hand and use your sketch to find the absolute and local maximum and mi...

A: Find your answer below