Determine the limit of the following 1.3) lim x--> 0 ( 1/x (1/3 - 1 / sqrt x + 9)) 1.4) lim --> Infinity (sqrt 9x2+ 4 / 6x + 1

Q: dy A-Find of the following: dx tan(5u) (1 + 2u)³ , u x. sin(x).csc(x) y = U = e4u

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Q: A smooth vector field G has curlĞ (0,0, 0) = 37 – 55+ 7k. - Estimate the circulation around a circle...

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. (Hint: factor the den...

A: Given, Evaluate ∫5x2+x+36x3+9xdx

Q: 3lnx +2dr A 3lnx B 2r4 D 3lnx +2x+ E None

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Q: Find the angle 6 between the vectors. u- (1, 1, 1), v- (5, -4, 3), radians

A: Angle between the two vectors can be found by applying dot product of two vectors.

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral. 

Q: 5) For p > 1, the root test applied to Ln=1 nº is inconclusive (C). 5.

A: Given

Q: (b) Then do the following: • If your answer is porsible, provide a specific example (a specific an) ...

A: D. Possible.     ex. an= 1n2  ⊙   limn→∞ 1n2 = 0 . Hence, an  converges.  ⊙  ∑n=1∞1n2 is converges b...

Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How fa...

A: Given; A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec.

Q: For the following functions: a) determine if f is continuous at x1, if not, determine the type of di...

A: The given functions are:1. fx=x+3if x≤3x3-20if x>3 at the point x1=32. fx=4-xif x≤44-x2if x>4a...

Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5, ...

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)

Q: 'ind the average rate of change of h(t) = 3 c on t-3 [1,1+ h]

A: Topic:- calculus

Q: Let f(x) = 6x + 13 – 15e". Then the equation of the tangent line to the graph of f(x) at the point (...

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Q: The alternating series (-1)" . converges. (You do not need to prove this, but you can if you 1 3" n ...

A: Here, the given series is: ∑n=1∞(-1)n13nn Now, the given series is an alternating series with 13nnn=...

Q: kdt, where k is constant k A True B) False

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Q: Graphs of the position functions of two particles are shown, where t is measured in seconds. (Enter ...

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Q: The indicated function y, (x) is a solution of the given differential equation. x?y" - 9xy' + 25y = ...

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Q: Two people sweep the floor. The table gives their sweeping rates, in square yards per minute (yd²/mi...

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Q: 4. A pizza is brought from the oven at 400 degrees into an 80-degree room. If y(t) is its temperatur...

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Q: 1. Use f(x) = x - x² +: +x and g(x) = 2f (x+1)+3 to do the following: a) Obtain a graph of fx) using...

A: As per the bartebly guidelines one question having 3 subparts are only to be solved. Please resubmit...

Q: A limestone stalactite grew in length at a rate of – of a millimeter per year. At this rate, how man...

A: Given the limestone is growing at a rate of 18mm per year i.e. 0.125 mm every year

Q: Scientists took 94 ice core sections from a glacier. Each section was in the shape of a right circul...

A: Given :Total ice core sections from a glacier=94Diameter of each section : 0.1mlength : 1 m

Q: Let a be a real number. Consider the series Σ where an = cos(n7) An, 2n +1° n=0 Find all a > 0 such ...

A: Given a series,

Q: Let f be continuous and have an inverse. Write F as the antiderivative of f, i.e., F(x) S ƒ (x)dx. U...

A: A detailed solution is given below

Q: Determine the point/s of discontinuity, if there is any, and the type of discontinuity at that point...

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Q: (a) Find a function that models the populationt years after 2000 (% for 2000). Your answer is P(t) =...

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Q: - In²(Ine*) dx A In²x B B Inr Ine D Inx2 E) None

A: topic - definite integral

Q: Complete the table. h(t) |t + 4| t -5 -4 -3 -2 -1 h(t)

A: The given function is: h(t)=12t+4 which is a modulus funtion.

Q: Consider the function shown below. V. 4 8 What type of function is shown in this graph? O A. density...

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Q: Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic equation for C = 15 a...

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Q: Obtain the general solution of the differential equation:y’ = cos2x cosy.

A: As per company guidelines we can solve first question. I hope that the given solution will help you....

Q: Determine if the sequence {a,} converges or diverges. Find the limit if the sequence converges. (- 1...

A: Here we have to determine whether the sequence {an} converges or diverges.

Q: f(−4) = −7,     f(1) = 4 (a) Write the linear function f that has the given function values. f(x) =

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Q: The table shows the results of a survey on the average amount of money d, in dollars, consumers woul...

A:  Given: X Y 25 42 28 36 33 26 35 22 42 8 Straight line equation is d=ax+b The normal...

Q: 31 'dt = +C 3lnz A True B False

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Q: d. One focus at (-3 - 3v13,1), asymptotes intersecting at (-3,1), and one asymptote passing through ...

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Q: A scientist initially has 40 mg of a radioactive compound that decays by about 10% each year (ie. af...

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Q: Find the absolute maxima and minima of the function on the given domain. T(x.y) =x +xy+y- 12x+2 on t...

A: Given

Q: A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate propo...

A: The drug is administered at a constant rate of rand is excreted (throwing off) at rate proportional ...

Q: 1. (a) Find the first four nonzero terms of the Taylor Series for the given function centered at a +...

A: i) f(x)=ex , a=ln 4ii) fx=ln x, a=3

Q: Integration is the reverse process of differentiation.

A: Given,            Integration is the reverse process of differentiation.To find : State true or fals...

Q: Evaluate the improper integral. (Hint: use the formula: S- dr = sin- +c)

A:

Q: Given a function whose graph is shown below. The function is continuous on[1,3]. Always True 1. O So...

A: The given graph shows that - The given function has a non removable discontinuity at x= 2 ( Non remo...

Q: The area, in square inches, of a certain right triangle is given by the equation A b(2b), where b is...

A: Given,          The area, in squares inches, of a certain right triangle is given by the equation A=...

Q: 3 1 321 A = B = 2 2 654 1 3 1. What is the size of A? 2. What is the size of B? 3. Is AXA defined? I...

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you ar...

Q: Is the function f (x) below continuous on [3, +∞)? (0, x > 0 x, 0 3 Choose Choose Choices Yes nuc No...

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Q: Hauata opens two bank accounts: a checkings account with balance b(t) and a savings account with bal...

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Q: The integral dx is Select one: O None. o o o

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Q: 00 Does the seriesE 1 converge or diverge? Give a reason for your answer. 15n - 1 n=1

A: 1P- Series Test:The series ∑1np = 11p + 12p + 13p + ...1. Covergent if p>12.Divergent if p≤12 Com...

Q: D. Evaluate et-2 tan vE 2t + 3 S 't² – 2t + 1 e2t

A: To evaluate: ∫et-2e2t, tan tt, 2t+3t2-2t+1dt=∫et-2e2tdt, ∫tan tt dt, ∫ 2t+3t2-2t+1 dt+A,B,C