What is the summation from n = 1 to infinity, of  (3^(n+1)) / 5^n + 1 ?

Q: Plot the curve c(t)=(2t−1,²+3). Then find the length of the curve for 1<t≤2 to two decimal places.

A: Curve is ploted and length of curve is obtained.

Q: 3) Find the following derivatives: a. y = 2x b. f(x) = 4x³10x² + 7x-15 c. g(x) = 3x(x² - 4)5 d. y =…

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Q: Consider the following. y 4 y=x³ - 2x -2 y = 2x (a) Find the points of intersection of the curves.…

A: This question is based on definite integral.

Q: Prove the following statement: 2² +23+24+... 2+1 = 2" +2-4

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Q: Use the formula к(t) 390 t¹4 k(t) (4 + 210 t¹3) = ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) = t²i+t¹5j X…

A: Use derivative for finding the curvature .

Q: ∫(x2+5)2 dx Evaluate indefinite anti-differentiation

A: Let's find.

Q: 4 P = 80x-2x²-xy-3y² +100y + X(12-X-Y) FinD Px, Pxx, Py, Pyy, Pxy = Pyx, fino x And y Fine Fine P

A: Here's the solution.... please have a look at it...

Q: Determine whether each of the following series converges. (Make sure to state which test you are…

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Q: 6. Find the intervals on [0,27) where f(0) = sin² (0) is concave upward/ concave downward.

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Q: Find f '(x), if f (x) = e−5x 5e O-5e^-5x 5e^-5x 5x

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Q: 3. Determine whether each geometric series converges. If the series 7n+1 2n converges, find the sum.…

A: Let's find.

Q: 4. Evaluate lim (cos x)¹/x². x-0

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Q: Find the indefinite integral. (Use C for the constant of integration.) 1₁ sin 20 de

A: This question is based on indefinite integral.

Q: d Calculate[r₁(t) · r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly…

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Q: 6) Given the function y = x³ - 3x. Find all the critical points, any local maximum or minimums, the…

A: 6)y=f(x)=x3-3xf'(x)=3x2-3f'(x)=0x2-1=0Critical points of f(x)     x=-1, x=1f'(x)=3(x2-1)f'(x)&gt;0…

Q: a graphing utility to construct a table of values for the function. Round your answer to two deci H…

A: Given query is to find the table using graphic utility.

Q: Compute the Jacobian for the change of variables given by u= x+y and v=x-y. O a.-2 O b. 1 2 O c. 1 2…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: 4x subject to the condition that y = 3 when x = 2. Preview TIP Enter your answer as an expression.…

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Q: Find the general solution to the differential equation. xy x-6 Preview TIP Enter your answer as an…

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Q: Evaluate the function at the indicated value of x =1. f(x)=loggx 8 -8 - 1011 8 0

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Q: √1² +25 -2 I dt

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: (b) 3, 1, 1 1 1 3'9' 27

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Q: Find the following using the table below. X 12 3 4 f(x) 3 1 4 2 f'(x) 4 1 2 g(x) 2 4 1 g'(x) 2 3 4 1…

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Q: Consider a triangle ABC like the one below. Suppose that b= 19, a=31, and B= 27°. (The figure is not…

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Q: Let f(x) = 3 + 2x². (a) Estimate the area under the graph of f, the x-axis, and the lines x= -1 and…

A: Solve the following

Q: The Smith's borrow $45,000 to purchase a new home. They finance the amount through a 25-yr mortgage…

A: Given problems:- 1. The Smith's borrow $45.000 to purchase a new home. They finance the amount…

Q: Please help

A: Solution: h(t)=12t +18t3/2 -6t2 when it reaches maximum upward velocity h'(t)=0

Q: 3. A snowball is rolling down a hill, getting bigger as it goes. Assume the snowball remains a…

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Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

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Q: Calculate the perimeter of each of the following [4] a) a parallelogram quit piece with sides 6%…

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Q: 10 F [TOF If f(x) dx = 16 and 5 Isro f(x) dx 10 f(x) dx = 5, find the following. S

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Q: Strontium-90 is a radioactive material that decays according to the function A(t) = A e scientist…

A: This question can be solved using the concept of exponential growth and decay.

Q: Calculate[ri(t) r2(t)] and [ri(t) x r2(t)] first by differentiating the product directly and then by…

A: r1(t)=6t i+ 4t2 j+ 4t3 kdr1dt=6 i +8t j +12t2 kr2(t)=t4kdr2dt=4t3 k

Q: D(x) = 62-0.1x

A: answer is in next step

Q: Compute the following determinant. -5 2 우리 1 6 0 X

A: We have to find the determinants

Q: Find an equation for the tangent line to the curve parametrized by x = e³t sin(πt) and y = et at the…

A: answer is in next step

Q: An airplane leaves City A and flies 144 km due north to City B. It then turns through an angle of…

A: The solution is given in the next step.

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.

Q: 1) Find the average value of the function f define by f(x)=√√√49-x²³² On the interval [0, 7] 2) Find…

A: We can use the equation to find average value of a function in an interval.

Q: 2. Given the first 5 terms below, write down the general term of the following sequences: (a) 80,…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

Q: Looking up, Jim sees two hot air balloons in the sky as shown. He determines that the lower hot air…

A: Follow the procedure given below.

Q: 1 Rewrite the logarithmic equation log4 16 -2 1 Gr= 16 04² = 21/160 4-2 4²/16--2 416 = -2 4-2= O O =…

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Q: me population of a colony of mosquitoes obeys the law of uninhibited growth. Use this information to…

A: Given query is to find the population after 4 days.

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 3 cos…

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Q: lim (i-8j+² k) 4 lim (r 1-8j+² k) = 1+ 16

A: We have to find the limit

Q: x² + 8x - 9 x1 x³2x25x + 6 t³7t² + 16t - 12 t44t³+ 4t² 4. lim 5. lim t-2

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Q: 8x³ + 4xy - y³ = 1

A: Given :