Problem 7 Proof that if lim f(x) exists then it must be unique i.e., x→a if lim f(x) = L and lim f(x) = M then L = M. x-a x-a

Q: Locate the absolute extrema of the function on the closed interval. In x, [1,4] 7x g(x) = minimum…

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Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

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Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Geometric Interpretations of Equations In Exercises 1-16, give a geometric description of the set of…

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Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: Find a rule for the derivative of the product of four functions f,g,h, and k. Use your result from…

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Q: The Eigen value of matrix p is (solve) ГО 0 Lo 1 0 0 1 -3 -4] (0,-1,-3) O (0,2,3) O (0,1,3) O…

A: This question can be solved using the concept of matrices and determinants.

Q: π Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for 6…

A: We have given a inverse trigonometric function of tan

Q: JO dt (Type exact answers.) The total amount of water that will drain from the pool is (Simplify…

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Q: a.) S (t² – 9) (4 – t²) dt from 2 to 3 b.) fx dx from 1 to 2 c.) f (x² - d.) f sin 0 de from 0 to…

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Q: We are interested in the first few Taylor Polynomials for the function = 8e +9e-x f(x) centered at a…

A: The given function fx=8ex+9e-x

Q: Your college newspaper, The Collegiate Times, has fixed production costs of $7000 per edition, and…

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Q: Let R be the region bounded by y = x², x = 1, and y = 0. Use the shell method to find the volume of…

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Q: Use differentials to approximate the value of the expression. Compare your answer with that of a…

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Q: Use any of the results in this section to evaluate the given integral along the indicated closed…

A: Cauchy’s Integral Theorem : If f(z) is an analytic function in a simply-connected region R, then…

Q: Verify if the indicated equation is an explicit or implicit solution of the given DE 1. y=csc(x+c):…

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Q: he time it takes an average athlete to swim 100 meters freestyle at age x years can be modeled as…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  take derivative

Q: X = [₁,√38² - 1 db y = v √314 - 1 dt, -2 ≤x≤-1

A: Firstly find  derivative of y then find length of curve

Q: Solve 4x - 5 = 19. O A. x= 10 OB. X=6 OC. x= 3.5 OD. x=8

A: We can find the answer as below.

Q: Increasing global temperatures raise sea levels by thermal expansion and the melting of polar ice.…

A: Given L(x)=0.02x3-0.07x2+8x where x is the number of decades since 2000.

Q: Given the values of f(x), g(x), f'(x) and g'(x) in the table, answer the following questions. x f(x)…

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Q: Find the position of a body moving on a coordinate line at time t for an acceleration a= dt² initial…

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Q: The Taylor series for f(x) = x³ at 4 is Σ cn(x − 4)". n=0 Find the first few coefficients. CO C1 =…

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Q: Solve the initial-value problem. dy = dx 4 √x for x ≥ 1 with y(1) = 3 The solution to the…

A: You must have idea how to find solution for differential equations.

Q: Evaluate 3 [²^{²} + √x² − ² + ³x² − ²) dx = x None of them 21.466 2.1664 -2.1646 -21.664 21.664…

A: Given problem:-

Q: if f(x,y) = √x² + y + 4, then find a a21 and ах ду х

A: If fx, y=x2+y+4, then to find ∂2f∂x2 and ∂2f∂y∂x.

Q: x(t) Find a plane containing the point (-4,3,-8) and the line y(t) z(t) = 8 - 3t 7 + 4t -8+ t

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Q: The Taylor series for f(x) = eª at a = -4 is Σ ²n(x + 4)" n n=0 Find the first few coefficients. со…

A: The solution is given below

Q: 17. Use the method of disks/rings to determine the volume of the solid obtained by rotating the reg…

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Q: The measure of the angle between the three- dimensional vectors u = (0, -1, -3) and V v = (2, 3, -1)…

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. y¹= x(2e + c) 2. y = Ae³x…

A: 1. y-1=x2ex+c Note:     Multiple questions are given, we are answer with only one question. If you…

Q: * Convert the polar equation to rectangular form r=7 (solve) x² + y² = 7 x=7 O Option 4 x² + y² = 49…

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Q: The symmetric equation of the line that passes by P(1, -1, 1) and Q(3, 2, -1) is: Select one: x-1 0…

A: This question can be solved using the concept of lines in three dimensional geometry.

Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

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Q: Solve DU 11 dx 4x+3 x³ +2x² + x

A: ∫4x+3x3+2x2+xdx=∫3x-3x+1+1x+12dx=∫3xdx-∫3x+1dx+∫1x+12dx=3lnx-3lnx+1-1x+1Add a constant to the…

Q: 1 2 1 Q2. If A = 200 31 2 find A¹.

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Q: Evaluate the definite integral. 2 cot-¹(x) 1 + x² 1 - 1 dx

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Q: etermine the net area.

A: NOTE: Refresh your page if you can't see any equations. .

Q: The intervals on which f(x) = x² ln x is increasing and decreasing, and the intervals of concavity…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: True or False: We have Select one: True False -8 √xdx = 64 3

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Q: The vectors u = (5, -4,0) and v = (-4,-5, 4) are orthogonal. Select one: O True O False

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Q: Find all solutions to 2 sin(0) 0= = - - 1 on the interval 0 ≤ 0 < 2π Give your answers as exact…

A: We can find the answer as below.

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(?) and y = r sin(?), and note that (x,…

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Q: answer = Σ n=0

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Q: : Use the chain rule to find the derivative of w= x² + y² with dw with x = cost + sint, y = cost-sin…

A: This question is based on chain rule differentiation.

Q: Surface integral is used to find Density O O Area Surface Volume O

A: We can find the answer as below.

Q: Which of the following is a unit vector parallel to the vector ? Select one: 2 0 8 1 4 <- 81¹ 81¹…

A: Let's solve.

Q: Let f(x)=1/3x+2. Use limit definition to find f'(x) algebraically

A: Solution of given question is written in below steps.

Q: Find the volume of the solid of revolution formed by rotating the region bounded by the parabola…

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Q: Let ā= and b = . Find 3a + 3b.

A: Given:a→=-3,-2,3 and b→=-3,5,2We need to find 3a→+3b→.