R Examine the discontinuity for each of the following functions. If the discontinuity it removable, redefine the function to make it continnou 5 if x>2 11. f(x)32 if x-2 -1 if x<2

Q: a dx Vax - 0 Vax

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Q: Find sin( ). (Hint: Use the half-angle formula.) arccos 3/10 V10/10 3V10/10

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Q: Determine

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Q: x = In(1– y²) 0<y <½ for Determine the arc length of the curve

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Q: If f(x) = 2x - 1, what is the equation of the normal line to the graph of fat (1, 1) O A. x - 6y = -…

A: 1) f(x)=2x3-1 at (1,1) 2)f(x)=g(u) and g(u)=u(x).

Q: y =f(x) Enumerate all discontinuities of f(x) and identify their types. If a discontinuity is…

A: We have to find the discontinu points

Q: Does the sequence {an} converge or diverge? Explain. Find the limit if the sequence is convergent. n…

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Q: 2.

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Q: Consider the following. -2 ifx -1 if x = -1 fix) = -2 y -2 -1 <-1 -3 Use the graph to find the limit…

A: We need to find limit at x→-1.

Q: Find an equation of the plane through (-8, –4, –5) that is 2 = t, y + 3 | perpendicular to the line…

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Q: 1 Find parametric equations for the path taken by a point the distance between the centre and the…

A: The given question has been solved in detail

Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: 3;) Find the välie of k isó that. the furnictioin %3D .kx*. .if. x 2 2. is. continuous .cvery iw…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation and use…

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Q: Assume that in the absence of immigration and emigration, the growth of a country's population P(t)…

A: In the absence of immigration and emigration the growth rate of the country is given by dP/dt = kP…

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Determine whether the lines L and L2 are parallel. L1: x= 2-3t, y = 3+ t, L2: x = 4- 12t, y= -3 +…

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Q: Follow the hint and solve the system. S2* + 2 l4* + 4Y 10 [Hint: Note that 4× = 22x = (2*)2.] 68 %3D…

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Q: 1. y=x3 - 6x2 y =0 Answer + 2. y =x4 - 2x y=0 12 -1+

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Q: 1) Determine whether the following series is convergent or divergent: 1 1+ 8 1 1 1 +... 125 27 64

A: We have to find the convergence test

Q: Evaluate the integral of e**+1 2xdx.

A: Given: I = ∫ex2+12xdx                                  ...........1 Formula: ∫eydy = ey+C

Q: 3 Simplify cos(arctan2). √5/5 no solution 2√5/5

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Q: 23. ** dx 4/5

A: Here ,we have given a definite integral.Now we solve it by using rules of integration. Then we put…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Use integration by part to obtain a formula for f x"e*dx and use it to find S x'e*dx. 3 5x

A: We have to find the integral

Q: A closed rectangular box with a volume of 375ft° is made from two kinds of materials. The top and…

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Q: 7. Find the general solution of the following differential equation: V1 + x²dy – xydx = 0.

A: Explanation of the answer is as follows

Q: Solve the given differential equation by separation of variables. csc(y) dx + sec sec2(x) dy = 0

A: Solve the given differential equation by separable method.

Q: What is the length of the latus rectum of 4x2+ 9y2 + 8x – 32 = 0? A) 2.3 B) 2.5 2.7 D) 2.9

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Q: b. f(x) = x - 3 x² – 9 2-

A: The given function is,   f(x)=x-3x2-9

Q: 2 : x = 1 + 3t, y = 3 – 6t, z = 5 – 3t are parallel and find the distance etween them. FOTE: Enter…

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Q: Find two unit vectors in 2-space that make an angle of 45° with 7i+ 4j. NOTE: Enter the exact…

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Q: Determine whether each improper integral below converges or diverges. a dx 2. S Vax – x 2

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Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Please see the answer below.

Q: Simplify tan(A+ arcsin?). O (2V13)/13 (3 V5)/5 (2 V5)/5

A: Given query is to simplify the expression.

Q: Find Duf at P. 2. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i+ 1 Duf = i

A: We need to find directional derivative at p.

Q: Choose the values that would complete the general solution for y = arcsin ( - V2) ±2nk 4 O O O O

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Q: Evaluate sin[2 arccos( -). -30/17 V(33)/17 -240/289

A: Please see the answer below.

Q: Simplify arcsin 3. 享、 3 no solution

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Q: Find the constant a such that the function is continuous on the entire real line. 4sin x if x < 0…

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Q: dy + y = y² sin x dx

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Q: Integrate: (7x³ + 4x²) dx

A: Given:- ∫(7x3+4x2)dx

Q: 2 (In x dx U.

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Q: Find the directional derivative of f at Pin the direction of a. f(x, y) = 4x* y²; P(3, 2); a = 3 i –…

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Q: Evaluate the integral of x(x – 5)1²dx with limits from 5 to 6.

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Q: 42) 2. 100 2. 3. 1.1 0100 1

A: Given data÷

Q: nd Solve:- Qz: Classify dy - 3x +(3メナリ』 = e Jス

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Q: x*-6x³+e* Vx dx

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Q: Evaluate the iterates integrals r*dA D = {(r, y) : 1<r< e, 0< y S In(x)} %3D

A: We will use simple Integration rules to solve this question.