Let f be the function given by f(x) = (x² – 2x – 1)e*. Find lim f(x) and lim f(x).

Q: If f(x) = x + 2 cos(x), 0< x < 2n, then f has a local maximum at A) x = 6. B) x = 6 11п C) x = 6. D)...

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Q: cos(3x) if x 1 if x = 0 or x = 1 Then f has removable discontinuity at 3 А) х 3D 0. B) x = 1. C) x ...

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Q: 1. Find the extremum of z = xy subject to x +y = 6.

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Q: If LR0} = F(s), then L{{3()}

A: We know thatL(f(t))=F(s)=∫0∞f(t)e-stdt

Q: X+2 sinx 2+5 lim

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Q: 1- Find the areas of the regions enclosed by the lines and curves: y=r-2 and y= 2 1- y = x* and y = ...

A: As per the guidelines we can solve 2 problems only 

Q: Find the exact value of sin COS 3 Write your answer in radians in terms of T. JT Undefined olo

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Q: The general solution of the DE y" + 4y' = 0 where y(0) =1 and y'(0) = 8 is O None of these y = 2 - 2...

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Q: Terential equation. (x + 6y²) dy = 0 (2x³ + y) dx – xdy = 0 ydx – %3D

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Q: Evaluate the given expressions. f(-1) = f(0) = f(1) =| Use technology to duplicate the graphs. Give ...

A: We are given the following equation. So, here f(-1) = --12=-1, f(0) = -02=0, and f(1) = 1=1. Note t...

Q: 5. A cube is located so that its top corners have the coordinates (-1, –2,2), (–1, 3, 2), (4, -2, 2)...

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Q: (c) ry-y dA where D is shown below.

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Q: lim

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Q: Find the limit . of functions cre given below b-) lim 1-V2-Cosx' Sinx a-) lim Vx+x - x = ? =? Xつ。

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Q: (cos(3x) if 3* x 1 if 3 + In x if 5 Then f has removable discontinuity at Let f(x) = %3D if x = 0 o...

A: This question is related to continuity of a function, we will use the definition of removable discon...

Q: The general solution of the DE y" - 2y' + 5y = 0 is y = cze*cos2x + c2e*sin2x y = cqe2*cosx + cze2si...

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Q: a. Which of these prime numbers would you have to consider as possible factors of 241 in order to de...

A: use the definition of prime number.

Q: Below is the graph of f(x). Given that: ms f(x)dx <n. Then n - m = 8- A) 8. 4. B) 16. C) 24. D) 48. ...

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the specifi...

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Q: If f(x) = x* +;x - x + 2, then f is concave down on %3D A) (0, 00) only. B) (-3,0) only. C) (-0,-3) ...

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Q: tind the derivatiues of given functions with respect tox. 12

A: Please refer to the image below 

Q: Given (3,7),  (6,18),  (12,35), what is the slope? The data are given as (x,y)

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Q: (5, 4),   (−5, −5) Using one point and the slope, write the linear equation in point-slope form, y ...

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Q: (x + y)dx + tan x dy = 0 (2x²y – 1)dx + x' dy = 0 %3D

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Q: Problems 2 – 3, verify by substitution that each given function is a solution of the given different...

A: To verify that the given function is solution of the differential equation 

Q: ху Find all second order derivatives for r(x,y) = 6х + 5y rxx (X,y) = 'yy(x,y) = | ] 'xy (X,y) = ryx...

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Q: 1. A statue 5 feet tall stands on a pedestal 9 feet high. If an observer's eye is 5 feet above the g...

A:  A statue 5 feet tall stands on a pedestal 9 feet high. If an observer's eye is 5 feet above the gro...

Q: F(x, y, 2) = xi + yj + 9k, s

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Q: Solve the following first-order partial differential equation using partial Laplace trasform: du + 2...

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Q: Find the limit. NOTE: Enter an exact limit if it exists. If the limit does not exist, indicate that ...

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Q: Find the differential of the function f (x, y, z) = sin x?y³z4. %3D O 2xy³z* cos a?y³ zªd« O 2xy®z* ...

A: Given f(x,y,z)=sin(x2y3z4)=ddx(sin(x2y3z4))We know that sin(x)'=cos(x)=cos(y3z4x2)*ddx(x2y3z4)

Q: Suppose that f has a domain of [7,19] and a range of [3,15]. (a) What are the domain and range of t...

A: Let's find. 

Q: 4 1 : Evaluate , x²ydxdy.

A: Please refer the attached image for complete solution.

Q: 5. Find the value ø(1) for a solution (x) to the initial value problem: (1+2x)y" + 4xy' – 4y = 0; y(...

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Q: 10. Solve the following differential equations. dy dy a) + 2.xy² = 0 b) -- y = 2x°y, y(1) =1 %3D dx ...

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Q: Find a pair of numbers whose sum and product are both equal to 32.

A: We have to find out a pair of number whose sum and product both are equals to 32. Let these 2 number...

Q: Kercise 1.2 -10 Evaluate the integral. xp A (xỉ +x²+ 1) dx 1 3 x(x'+2x+ 1) dx 3

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost ot...

Q: Give the formula for a function which has vertical asymptotes at x=7 and x = -6 but is otherwise con...

A: A function has vertical asymptotes at x=7 and x=-6 but is otherwise continuous.

Q: Evaluate the indefinite integral. x18 sin(x19) dx

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Q: Use the function in the picture to answer the following questions: 1. What is the average value ove...

A: The given function is: f(x)=1x Now, the average value f the function on [a,b] is given by: faverage=...

Q: 2. Find the relative extrema of y = 3x – 5x3 – 225x1 + 70x2 + 23

A: Explanation of the answer is as follows

Q: b) Find the volume generated by revolving the region x = y and y=x-2 about y-axis. (Sketch the regio...

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Q: Suppose 2<f'(x) < 4, for -1 sxs1. Then f(1)- f(-1) is between A) 4 and 8, B) 8 and 16. C) 0 and 4. D...

A: Given  2≤f'(x)≤4 for -1≤x≤1Then We know thatf(1)-f(-1)2=f'(1) (by definition of derivative)We know t...

Q: 2. Below is the graph of f(x). For each of the given points determine the value of f(a), lim f(x), l...

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Q: The U.S. Federal income tax is a function of taxable income. Write T for the tax owed on a taxable i...

A: Here, from the given table the function for the income tax T as a function of taxable income x is: T...

Q: SI-1 Review of change of variable in integration. In this problem, a, b, e, and d are constants and ...

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Q: Family of circles centered at the lint y = 2x k 2h

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Q: Suppose that the functions and g, with L and La at r a as shown below. approximations Then lim a9(x ...

A: option (e) is correct 

Q: Use spherical coordinates to evaluate f[[, 3e(a+y´+z²)°/² dV, where E is the region inside the spher...

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Q: 10- Find the volume of the solid generated by revolving the region bounded from the left by the y-ax...

A: Solution is given below:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.