CONTINυITY (c) The function f (x) is defined in the interval [-1,6] by 3-x, -1

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A: Given: ∫tanln4x2xdx Integrate the equation we get, Consider, u=ln4x2 du=2xdx Substitute in integral ...

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A: (a) To test the convergence of the series ∑k=2∞1kln k5-1k5, we will analyze the convergence of the s...

Q: у %3D Зx5 — 15x4 + 20х3 + 3 -

A: Given : y=3x5-15x4+20x3+3   To Find : x & y- intercept of the given graph

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Q: To evaluate the possibility of using pyramid-shaped vessel, the rate of change of the dimensions wer...

A: This question can be solved by using rate of change of physical quantities.

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A: Given equation, yy=as where, y is Pinocchio’s nose length (in inches) s is his lie count a is a magi...

Q: Name: Section: Find the derivative of the following. Show your solutions. 1. What is (3x) ? 2. What ...

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Q: -1-0. 1) Write f(x). 3) Find D & R 4) Sketch f(-3t+3) 5)Find D & R for the function of point 4 2)Fin...

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Q: Find the Maclaurin polynomials of orders n = 0,1, 2, 3, and 4 and then find the nth Maclaurin polyno...

A: f(x) = 16 ln(1+x)f0(0) =16 ln(1)f0(0) =0f1(x) =f'(x)=16x+1f1(0)=16f2(x) =f''(x)=-16(x+1)2f2(0)=-16f3...

Q: 2. Use the Intermediate Value Theorem to show that 2.x - 3 if – 3 0 has a zero on the interval [-2, ...

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Q: Find dy/dx for the following function: X+ tan (xy)-0

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Q: Is the series convergent or divergent? Prove in no more than two sentences. +oo - n T1-n n=1

A: ∑n=1∞ (πnπ-1n3)(series with increasing terms)limn→∞(πnπ-1n3) =∞-0  =∞   

Q: The area of the rectangular piece of cardboard shown below is 209 square inches. The cardboard is us...

A: Given problem:- The area of the rectangular piece of cardboard shown below is 209 square inches. The...

Q: 2) An agriculturist wanted to plant seven different organic crops in a small field. To properly stud...

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Q: 3 In x + 1 dx x (In x + In x) Evaluate A In lin?x + 1 + c Bn in°x + In x + C ©nlin³x + In x| + c D 3...

A:     ∫3ln2x+1xln3x+lnxdxLet u=ln x.=∫3u2+1u3+uduLet v=u3+u.=∫1vdvSubstituting back we get,=lnln3x+lnx...

Q: 5. Find the area of the region enclosed by one loop of the curve: r= 4cos(3Ø)

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Q: Find the radius of convergence and the interval of convergence. Σ k(k+ 1) k=1 1) First apply the Rat...

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Q: Find the percentage error in computing u = Vx at x = 2.45, when x is 4

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post ...

Q: Find the centroid along the y-axis of the plane area bounded by the equation y^2=4x, x=1 and the x-a...

A: Given curve is y2=4x ,x=1

Q: 3(1+x²)-1/2, y(C

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Q: Consider the following sequence: {an} = an+1 Use the ratio an - to show that the given sequence {a, ...

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Q: sin(2a)dx + cos (3y)dy 3 0, у(т/2) — п/3 ||

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Q: The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventua...

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Q: Differentiate f(æ) = 27. 1.

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Q: Prove that the sum of the first n natural numbers is given by this formula: n(n + 1) 1+2 +3 +. .. +n...

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other questions as...

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: We find out the Taylor series of e5x at c=0. Follow 2nd step.

Q: Graph the two equations x+y= 0, and y = - (x-1) and find the points in which the graphs intersect

A: 1. Given x+y=0y=-xtf x=0,y=0if x=1 ,y=-1if x=2,y=-2Graph passing through origin .2. y=-x-12if x=0,y=...

Q: u+1 Using u-substitution, the integral Jf(x)dx reduces to a new integral glu) du. If glu) = , evalua...

A: Given  g(u) = u+1u and  ∫f(x) dx = x + lnx-1 + C

Q: tan x 2. (a) lim e →号一 (b) lim sin (tanh 3x) エ→十0

A: limx→π2-etanx

Q: 2. f(x) = Va +æ + 1

A: Here, the given function is: f(x)=x2+x+13 Now, f'(x)=13(x2+x+1)13-1(2x+1)        =13(x2+x+1)-23(2x+1...

Q: Determine whether the given series is absolutely convergent, conditionally convergent or divergent. ...

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Q: O : (2r-3)/ar- 12x²+ 7 – 2 im |2x*-3 + Vart- 12r²4 7|} +C V4r4– 12r2+7|}

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)*+1k! (2k ...

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Q: 3 In?x + 1 Evaluate x (In³x + In x) 3. A 3 In |in3x + In x| + C B B In in3x + In x| + C -In lin?x + ...

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Q: Use the difference a,41 - a, toshow that the given sequence (a, ] is strictly increasing or strictly...

A: We can solve the following problem as:- Here N= {1,2,3,.......n...}

Q: dx Given: 7-ge-2x. Using u-substitution and transforming the integrand, find du. A 18e-2xdx B - 18e-...

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Q: 4. Find the area enclosed by the curve: x=t2 – 2t, y= vt and the y-axis

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Q: Do the following: (a) Construct the table of values; (b) graph the function; and (c) find the indica...

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

Q: The sequence

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Q: Given: V5x-3 xdx. If we let u= 5x - 3, which of the following u-substitution formula is applicable? ...

A: Given  ∫5x2-3 x dx

Q: u+1 Using u-substitution, the integral Jf(x)dx reduces to a new integral g(u) du. If g(u) = , evalua...

A: We have to find value of f(x)

Q: Determine if -1 CSC if 0 1 is continuous or not at r = and 1. If it is discontinuous, identify the ...

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Q: (т — 3)" - Determine the interval of convergence of 2n +1

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Q: ergence and the interval of convergence. Test for Absolute Convergence to the given series. The

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Q: 3. a) Find the percentage error in computing u = Vx at x = 2.45, when x is 4 %3D b) | If Ax = 0.005,...

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Q: Factor the difference an+1 - an to show that the given sequence {an} is strictly increasing or stric...

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Q: Determine whether the given series converges or diverges n2 Σ 2n In n n=1

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Q: 2) Find the tangent to the curve y 2 tan at x 1.

A: A detailed solution is given below.

Q: /4x+ – 12x² +7 xdx . Evaluate the integral A) -(4x4 – 12r²+7)/2 +c 24 © ! (21--3)/- 121+7 – 2 m 21--...

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Q: Find the limit by rewriting the fraction first. ху — у — Зх + 3 lim х - 1 (x,y)>(1,4) x+1 ху — у — 3...

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