Find the sum of the convergent series. (b) (sin 1)" n=1 9 27 (c) 8+6+;+ Σ (2n + 1)(2n + 3)

Q: 5. Sketch the graph of the logarithmic function f(x) = log, x, State the domain, range and asymptote...

A: This question is based on Logarithmic graph and it's properties.

Q: Question 16 In (ale) (2-sec2x)emlesec'x sec( 3A – x) What should be the value of A for dx to be inte...

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Q: e* What is the integrable form of dr? ex - e du du 1) 2 du du

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Q: Let a, b be real numbers and consider the integral (ax² + b) cos(x)dx. Using integration by parts wi...

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Q: Carbon decays exponentially. How many grams of the carbon will be left in 139 years, if 123 grams we...

A: Initial amount P0=123 grams time t=96 years Amount left after 96 years =P=66 grams Exponential decay...

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Q: Peter likes to drink coffee once its temperature reaches 60 degrees Celsius and will not burn him. I...

A:   note : i can ans 1st and 2nd part and remaining part not related to this question so pls reroute i...

Q: cos-sin0 d0 has the form –-F(0). 2 2 The resulting integral of sin- +C. What should be the value of ...

A:      ∫sinθ2cosθ2sinθdθ=∫12sinθ sinθdθ=∫12sin2θdθ=12·∫1-cos2θ2dθ=12·12·∫ 1-cos2θdθ=12·12∫ 1dθ-∫cos2θd...

Q: 8969 2. find 121 detA)? OY

A: As per our guidelines we are suppose to solve only first question if the multiple questions are post...

Q: xcos³x² The S dx is 1-sin x? sin?x² + C {c}sin x² +sin²x² + C {D}sin x? –sin²x² + C { A} sin x² 2 4 ...

A: This question can be solved using integration by substitution.

Q: 1. y= x - x'cosx + 2xsinx + 2cosx

A: solution:-(1)y=x3-x2cosx+2xsinx+2cosxy'=ddxx3-x2ddxcosx+cosxddxx2+2xddxsinx+sinxddxx+2ddxcosx=3x2-x2...

Q: A. What would be the initial population of the mosquitos colony? B. What is the population of the co...

A: Substitute x= m in the equation to get p(m)

Q: Cost and Revenue functions C(q)=q3−11q2+55q+5000 and R(q)=−3q2+2500q​, what is the minimum marginal​...

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Q: FIND THE ARG CZ) OF THE COMPLEX NUMBERS 2

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Q: Let P(t) = (x,y) be the terminal point on the unit circle that corresponds to the real number t. Fin...

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Q: Find the general solution to this homogeneous equation using the auxiliary equation method y”+ 4y’ +...

A: The given differential equation is  y''+4y'+8y=0.

Q: Use the First Derivative Test to find relative (local) maximum points points, if any, of the given f...

A: given 

Q: (2- sec?x) " sec(3А — х) e In (a le) sec3x -dx to be integrable using What should be the value of A ...

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Q: Q4) Find the Asymptotes of the following functions: x³ – 4x² - 1) y x² – 2 x² – 4 2) f(x) : %3D x² –...

A: Solution is given below

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the c...

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Q: Determine the convergence or divergence of the following series. 1 (a) Σ (Use Integral Test.) n(ln n...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: The expression below is an evaluation of which integral? * 1 2 + 83 In|w| In|u² + 9| +c 18 2+ w4 dw....

A: option 3 is correct, see the solution, please thumbs up, if your doubt is cleared.

Q: Check if the following is true or false: 3 (e" – 7)da = e Select one: O True O False

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Q: Use an appropriate test to determine if the series ) 2n converges or diverges. n+ en

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Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: What is the integrable form of sin-cos-sin0 de? 2 2

A: A detailed solution is given below.

Q: 4. y=x

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Q: 10. f"(t) + 3f'(t) + 2f(t) = 0; ƒ (0) = 1 and f'(0) = 0 %3D %3D

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Q: dx

A: Given problem:-

Q: dy +x =

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Q: Solve for the angle in the equation. * a. sin (30 + 72)° = cos 48° b. 4 sin? (§) + 8 cos () – 7 = 0 ...

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Q: (2- secx) secx sec(3A – x) eIn (xle) What should be the value of A for to be integrable using the fo...

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Q: The number of solutions to cos 0 = – c, with 0 < c < 1 and O 2 Infinitely many

A: This question can be solved graphically.

Q: Find lak| for the series. 00 k k k + 12 k=0 (Express numbers in exact form. Use symbolic notation an...

A: The series ∑k=0∞kk+12k

Q: Select the answer that is equal to e#/² f(x) dx. Show workings. A. 2e*/2f(x) +2 | e=/² f'(x) dx B. e...

A: To solve the problem we use integration by parts formula. From integration by parts we get: ∫uv dx =...

Q: O Use the divergence theorem to evaluate F-dS, where F (x, y, z) = zxi – e"j+ 4zk and S is the surfa...

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Q: 2 Determine the equation in the form (x) kx for the function with a vertical %D asymptote at x = 1 a...

A: The function with vertical asymptote at x=1 and y-intercept at -1.

Q: 2. Let by = cos and cn = cos for all n e N such that n > 2. Determine whether the given n – 1 series...

A: Using Telescoping series. 

Q: 2. For the line through P(3, 2, – 1 ) and Q( – 2, 1, – 4 ), determine each of the following : a) vec...

A: For the line through P3, 2, -1 and Q-2, 1, -4, to determine each of the following: a vector equation...

Q: Consider the points A(1, -1,4), B(2,-3, 2), C(-1, -2, 2), and D(4, 3, –6). (a) Find the volume of th...

A: The answer is shown in step 2.

Q: $ Solve and convert to rectangular form. ti sin sin )

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

Q: dx -In[F(x)]+ C. What is F( 3) if c = 0? For (x+x³)(x Tan-!x + 1)

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Q: Find the area bounded by the x- axis and the graph of the function f (x) = 4x² + 8x +1,0 <x 3. (4 II...

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Q: 7. g(t) = tỉ %3D

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: u = 2i + 3j + k v = i+j+ 4k w = i+ 3j + 8k

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Q: 4) Factor fully. a) x3 + 4x² + x – 6 b) 2x3 – 9x² + 7x + 6

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Q: 10. Find, among all right circular cylinders of fixed volume V, the one with smallest surface area (...

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Q: dr = b(cos Odr +r sin Ode) Ans. r = c(1-bcos 0)

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

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