lim x⟶0−        f(x)= B) lim x⟶0+         f(x)= C) f(0)= D) Determine whether the function f is continuous at x =0.   If the function is not continuous, state the type of discontinuity.

Q: Solving by variation of parameters y"-3y' x the general solution is: O None of them O c_1+c_2…

A:

Q: 5. Prove lim,40 V2r +I= 1.

A: Given :limx→02x+1=1

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A: We have to find solution

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A: Let A and B denote the events of guessing the correct option of question 1 and question 2…

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A: Given query is to find the Indicated time.

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A: Consider the series 6m + 3m + 0 + (-3m) + (-6m) ...

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A:

Q: Green theorem satisfied if the region C is closed True O false O

A: Greens theorem

Q: Using the substitution x = sec 0, 2dx Jx?Vx² – 1

A: We can find the solution to the integration as below.

Q: A Moving to another question will save this response. buestion 9 Consider this expression: -1 sin…

A:

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A: Given query is to find indicated derivative.

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim Cos n-00 2n i= 1

A:

Q: Evaluate the following expressions. Your answers must be exact and in simplest form. (a) In e l = -1…

A: We can answer the questions as below.

Q: Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for…

A: 2+52+3+72+......9

Q: The solution of the Ordinary Differential Equation 4y" - y' - 3y = 0 if y(0) O and y'(0) %3| 7 - is:…

A:

Q: The series 7 2n E,(-1)" 4 n= is absolutely convergent. Select one: True O False

A: Root Test : Suppose we have series ∑ an .Define,                          L = limn→∞ an1n .Then ,(…

Q: The value of E +2i+1 is i-1 139 146 124 90

A: Solving

Q: The technique used to prove that dk =- 3x + 3V3 tan" + C %3D x2 + 3 3 is O Integration by Parts O…

A:

Q: Question 2 ( Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y'(0) = 3. (a) Use the…

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Q: 8- Consider u=x², v=1/u+1 and w=vv find dv/dx

A:

Q: Solve the following quadratic inequality: a“ – 6x + 8 <0 Write your answer in interval notation.…

A: First we shall factor and find roots of quadratic equation then figure out intervals in which…

Q: 10 8 Consider the function f(æ) Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) :

A:

Q: 5.1. Find the area enclosed by r = V cos(0). (Ignore the r= 2 cos(0) for this part of the problem.)…

A: 5.1) To find the area bounded by the curve r=cosθ

Q: a) [*. : Determine whether the series 1 Σ (2n – 1)4 n =1 is convergent or divergent.

A: To determine whether the given series is convergent or divergent

Q: الإنجليزية Q3: It is required to find the general solution of the following system dx =y+z dt (1) dy…

A: Second-order linear equations with constant coefficients. The generic form of an equation like this…

Q: The solution of the ordinary differential equation -y(4) + 4y" = 0 is: O c_0+c_1 x+c_2 e^(3x)+c_3…

A: Given -y(4)+4y''=0To find solution of Ordinary Differential equation:

Q: -6- They" for y = -9 3x-5

A:

Q: The region below is bounded by y = 4/T, y = 0 and r = 4. 10+ 8. 7. 6 4. -3 -2 4 -2+ If we use…

A: topic- area bounded by curves

Q: Using two or more complete sentences, explain how to find the sum of the geometric series. n-1 4 n=1

A: Infinite gp

Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b). If the…

A: We have to check if Mean value theorem can be applied or not.

Q: Find the following limit or state that it does not exist. x - 4x +3 lim X-3 x-3

A:

Q: Using decomposition into partial fractions, 4x2 + 2 dx x(x² + 2) is equal to In|x (x² + 2)| + C…

A: Solution is given below:

Q: Using appropriate substitution, [sec (2x) – 1] tan(2x) dx is equal to

A:

Q: Let x'y"-7xy' + 16y= 0 be an ordinary differential equation. Knowing that y,(x)=x* is a solution of…

A:

Q: 4 Consider the following geometric series: 2 + 8. 16 + ... Identify a and r, find a formula for the…

A: solution:-2+43+89+1627+...first term, a=2common ratio, r=8943=23general term, an=arn…

Q: compute J, f(x)dx 2x if x < 1 f(x) = { 4 if x2 1

A: Given query is to find the value of the integral.

Q: 12. Consider the region R bounded by the line y = 37 – 7x and the parabola y = 27 – x² . %3D Find…

A:

Q: The solution y, of the homogeneous differential equation y() + 36y" = 0 is O None of them O c_1+c_2…

A:

Q: 2- A hot-air balloon is moving vertically up and down so that its height relative to the ground is…

A: We have to find the velocity and acceleration.

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A:

Q: Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist,…

A: f(x)=(x+5)23  f'(x)=23(x+5)-13  f'(x)=23 (x+5)3Let's understand f'(x) as a different…

Q: The maximum value of x + y + z subject to the constraint x² + y² + z² = 1 is Write in decimal form…

A:

Q: 4 8. + 6. 16 Consider the following geometric series: 2+ + .... Identify a and r, find a formula for…

A: The given series is  2+4/3 +8/9 +16/27+...

Q: Using decomposition into partial fractions, 4x2 + 2 -dx x(x² + 2) is equal to In|x (x? + 2)| + C…

A:

Q: 5. The partial graph of y = logb x passes through the point P (2,0.5) and Q (a , 2). The value of a…

A:

Q: Evaluate the summation (2i - 1)? - i=1 155 162 165

A: Topic = Algebra

Q: Solving by variation of parameters y" – 3y' = x the general solution is: None of them c_1+c_2…

A:

Q: The terms of a series are defined recursively by the equations az = 5 5n + 2. an. an+1 4n + 11…

A: Here, the given series has: a1=5, an+1=5n+24n+11an

Q: Using Sandwich Theorem, the sequence 2 cos? n + 1 an = 4 - diverges converges to 0 converges to 2…

A: Use range of cos x which lies in -1 and 1

Q: 1+x dx V1-x

A: