For the function f, how would you remove the discontinuity? In other words, how would you define f(2) in order for f to be continuous at 2? x²-x-2 f(x) == x - 2

Q: Evaluate the following dx (x - 1)(x-2)(x-3) integral s

A: We need to evaluate integral.

Q: Q5) Solve the following using Trapezoidal rule with n6 f(x) = f*xinx. dx

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Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: This question can be solved using the concept of derivatives.

Q: 8) Consider the solid Q that is generated in the first octant by the surfaces S₁: (x - 2)² + (y-2)²…

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Q: 1. Evaluate √2 √4x² dx using a trigonometric substitution.

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Q: A projectile is fired in the air from a height of 125 feet. Its velocity (in feet per second) t…

A: (d)     Given that                            u = 233 feet   at  0 feet         We have to…

Q: Function do you know from calculus is such that its first derivative is itself? (Do not use the…

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Q: Use limits to identify all the linear asymptotes of r³ - 3x - 1 x² f(x) = 2x² +1 x² + 2x +1' x < 0 x…

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Q: Lucy draws a line on a coordinate plane. Which transformation will always result in a line…

A: Reflecting a given line firstly over the x-axis and reflecting over y-axis , both reflected line…

Q: 1. An object has a mass m = P+1 3p+1 and density p= m P-1 Determine the volume v, where p = [K]…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Q3: Fill in the blanks in the following: A. If u= (1,6,-8) and v=(4,-2, -1) the xu B. The inverse…

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: m d 4. f(x) = ln 3/4-x x-bf + bf)

A: ddx9+9-x

Q: 3x²y dx − (x³ + y³)dy = 0, y(1) = −2 -

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Q: Consider h(x, y, z) = cos (ry) + e + In (zz) at the point P (1,0, P(1,0,¹). mine the following: (a)…

A: Given problem:-   consider h(x,y,z)=cos(xy)+eyz+ln(xz) at point P(1,0,1/2)  Determine:- (a) the unit…

Q: Use the trapezoid rule with n = 60 to approximate the sum in addition to providing the…

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Q: for the function below, the domain and the range is respectively -2+√1-x

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Q: Find the Taylor polynomial of degree 3, centered at   a = 0   for the function   f ( x ) = √ x + 7

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Q: C-The result of the following limit is sin 1² lim t 1-0 Oo O infinity 02 O anther answer

A: We can solve this as follows:

Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

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Q: Solve the initial value problem ди Ә дудх (1) ди - 4- = 0, (0,y) =2sin y, u(x,0) =х. ду

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Q: 1. There are initially 95 mg of a decaying radioactive substance, and after 10 hours there are 68…

A: Given: Initial amount of the radioactive material= 95mg After 10 hours amount is =68 mgTo find: Half…

Q: Find the roots of the differential equation: y" +4y' +6y= 0

A: See the details solution in below

Q: 3 Q19- if z = z =- 4x³y sin sin (x³y) find d əx

A: Given problem:- if z = -4x3y sinsin(x y) find ∂z/∂x

Q: for the function below, the domain and the range is respectively y = x²/5

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Q: Solve the differential equation: dy y+ = dx

A: Given query is to find the solution of the differential equation.

Q: Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, da where A is a positive constant. The…

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Q: Determine whether the differential equation (7x² − 2xy + 2) dx + (4y² − x² + 7) dy = 0 is exact. If…

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Q: 3- prove that w = w yx if w = xy² + xy +

A: Given problem:- w=xy2 +x2y3+x3y4  Prove that wxy =wyx

Q: A- for the function below, the domain and the range is respectively y = |x|- 2

A: Topic = Functions

Q: 5. Use the Squeeze Theorem to evaluate lim sin z 2 1-00

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: ) R.J&M Company manufactures furniture such as sofas and tables. In their current inventory, a total…

A: We have to find the number of sofas and tables.

Q: The height (feet) of an object launched in the air t seconds after launch is given by s= - 16t²…

A: The height of  the object,   s=-16t2+288t+9

Q: Evaluate the following integrals 32-1 x + 2 dx +-² +1

A: SOLUTION-

Q: Find the value of k so that the given differential equation is exact. (7xy³ + cos(y)) dx + (2kx²y² -…

A: Given

Q: Find a particular solution yp of the following equation using the Method of Undetermined…

A: answer is in next step.

Q: The velocity of a particle on the time interval 1 ≤ t ≤ 4 is v(t) = t³ - 1, where v(t) is in cm/s.…

A: topic- average of function over interval

Q: When fully multiplied out, what is the 8th term of (x-3y)¹22 A -1,732,104x5y7 B -1,082,858x³y7 C…

A: We have to find out term

Q: Evaluate the following - ² (x − 1)(x − 2)(x-3) integral

A: Given problem:-

Q: Solve the boundary value problem, if you have : 4y" + 3y = 0; y(0) = 1; y(n) = 0

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Q: dy x3 dx 2+y²

A: Let's solve given diffrential equation.

Q: The Value of the integration for the below function shown is : I se sec²2xdx

A: See the details solution in below

Q: 5-10 + 15-20+.... -500

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: Here we have to use Euler's method to obtain a four-decimal approximation of the indicated value.…

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: The answer is given below:

Q: The value of θ, where 180º ≤ θ ≤ 360º, in the equation 2cos2θ + cosθ =0 would be? i) θ = 90º, 120º…

A: We want to select the correct option.

Q: (vii) 5.001 = mpQ (viii) 5.0001 MpQ = (b) Using the results of part (a), guess the value of the…

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Q: use Green's Theorem to evaluate the f(x² - 3y) dx + 3xdy where C is a circle x² + y² = 4 and…

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Q: help

A: We will solve the problem.

Q: dy Give the coordinates of the point where y = sin(t)- t³ O (0,0) O (0.535,0) O (-0.535,0) (0, 1) is…

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Q: Q1: Answer 2 branches only A. Find the general solution of the following Initial Value Problem (IVP…

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