For the continuous function f(x), if f’(-4) does not exist, then x=-4 is a critical point.

Q: f (x) = x² – 2x ; a = 1 f (x) = |x| ; a = 0 f (x) = ; a = 0 3 x+1 f (x) = ; a = 3

A: f(x) =x2-2x  ,From graphContinuous and differentiable at a=1

Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

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Q: y" +y = 0, y(7/3) = 2, y(T/3) = -4. = -4.

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Q: a) Find the intervals where the function f(x) is increasing or decreasing b) Find the intervals…

A: Follow the procedure given below.

Q: 3+5n 1. an n+n

A: the given sequence,an=3+5n2n+n2

Q: Find the intersection points of the pair of ellipses. S4x2 + y2 = 4 (4x² + 9y2 = 36 %3D ([ (х, у) 3…

A: We know that standerd form of an ellipse is :- (x-h)2/a2  + (y-k)2/b2 = 1     Here i attached the…

Q: Find the volume of the solid generated if the region bounded by the parabola y2 = 4px (p > 0) and…

A: Given

Q: (- 1)" Σ n =1 n 3+5 8.

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y,…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti +t²j dt

A: We have to calculate value of given integration

Q: OR = {(r, 0): 0 <r< 6 cos(30), 0 < 0 < n}

A: Follow the procedure given below.

Q: QUESTION 1 Find the magnitude and direction of the vector acceleration when t=2 seconds for an…

A: Position vector:r(t)→ =t3, 1-t2Velocity vector:v(t)→ =r'(t)→ =3t2, -2tacceleration…

Q: (a) Suppose that f is differentiable, positive and decreasing on (a, b] and has no critical points.…

A: Given problem:-

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

Q: Knowing that harmonic series is divergent, which of the following series is also divergent by Limit…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: Given : r(t) =36-t2i + t2j-2tk   To Find : Domain

Q: x^n dx=x^(n+1)/(n+1)+C is not possible when    a. n=0   b. n=1   c. n=-1   d. n=2

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Q: yA (b) Economists study two functions: R(1) and C(r) which are the revenue and cost when r units of…

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Q: Verify Green's Theorem by evaluating both integrals aN aM y2 dx + x2 dA ду ax for the given path. C:…

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Q: Use the comparison test to test the series n2- 1 n =1 クタ

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Q: Use Exact Differential method ( Rule II) to solve : (x² – y²)dy = xy dx.

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Q: 4. Find the critical numbercs) for gx) =IRCX+1) t, en cuaracterize ealh, one as 1ocal min, or…

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Q: 10 The following series is divergent. (-7)-/2 + 17 Select one: O True O False

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Q: Simplify tan(arccot0).   undefined 0 pi/2

A: Topic = Trigonometry

Q: s representation for f(x) 1+ x3 ° find the exact the power series obtained 2.

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Q: 4y" – 0 +12y' + 9y - 0 e. f. y" – 6y' + 9y – 0

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Q: Evaluate the definite integral. Use the integration capabilities of a graphing utility to verify…

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Q: g(t) = 4T - n, where n is a constant. Suppose we want to evaluate | 9(t) dt. O dt | Va dt + dt - 4 a…

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t=0 T(0) = N(0)

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: We have to find volume of solid formed by rotating the given equations about X - axis.

Q: Set-up the integral for the area A(R) of the region R bounded by the circles y2 + x² = 4, and y2 +…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: _9. Which of the following is equal to fo°dt? A. e C. ex+C D. et +C B. e° +C _10. What should be the…

A: Given data÷

Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

A: This question is based on integration by parts.

Q: Determine whether the following series is convergent or divergente: (- 1)" n = 1 n'+5

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Q: I need help with all of these problems

A: Given

Q: a L. determine whether the series Use the Integral Test to 2 Σ n=1 (2n – 1)4 is convergent or…

A: Solving

Q: x+1 dx J-1

A: ∫-10x2x+1dx

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Using she'll method, volume is evaluated.

Q: Find the volume of the solid generated when the region enclosed by y = Vx, y = 6 – x, and y = 0 is…

A: This is a problem related to integration. Based on the integral formula we will solve the volume by…

Q: what is of the waximal domain gla) = Inf2x)

A: Maximal domain is the largest set of real numbers for which the function is defined. The given…

Q: Graph 1 Graph 2 Graph 3 24y 6. 4+ 4. + -8-6-4 4 6 -8 -6 4 4 6 2. -4+ -4- -6. -8 -8- OYes OYes ONo…

A: Given that -

Q: O (1, 5) О (-о, 1.5] O (-1, 4) О (-3, 2)

A: Let's find.

Q: 9 Determine whether the series 9. 9. +...+ 9. +... is convergent or 100 1002 1003 100" divergent. If…

A: 9100+91002+91003+.....+9100n+...common ratio:a2a1=a3a2=1100First term: a=9100common ratio:…

Q: sin t = (eit – e-i#)

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Q: Which of the following series is convergent? 2 n 3 n=1 3 n n=1 O None of them. n 4 n=1

A: Check the condition of convergence and divergence.

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x' + x + 1,…

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Q: Use the comparison test to test the series i n²-1 n = 1 n* 4

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Q: The figure shows the level curves for a function f over a square region R. Approximate the integral…

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Q: Set-up the integral for the area A(R) of the region R bounded by the circles y2 + x² y2 + x² = 16,…

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