Find the 100th term of the arithmetic sequence with first term 5 and eighth term 19.

Q: Evaluate the integrals . Some integrals do notrequire integration by parts. ∫1/x (ln x)2 dx

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Q: 3 = 4- 2y + - dx

A: The differential equation is,   The figure below represents the vector field of the differential eq...

Q: A 2,916-liter cistern is empty when water begins flowing into it (at t=0) at a rate (in L/min) given...

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Q: Speed and arc length For the following trajectories, find the speed associated with the trajectory, ...

A: Given Data The function is r(t)=<13 sin 2t, 12 cos 5t, 5 cos 2t>. The interval is 0≤t≤π.   Dif...

Q: 27-40 - Graphing Exponential Functions Graph the function, not by plotting points, but by starting f...

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Q: State the domain and range of ƒ1x2=1x2 + 12-1.

A: This function can have all real values of x. So the domain is all real numbers.   

Q: Perform the indicated operation(s) and write the result in standard form : (8 + 9i)(2 - i) - (1 - i)...

A: Given  The equation is (8 + 9i)(2 - i) - (1 - i)(1 + i)

Q: Find the solutions of the following clairaut differential equations.

A: The clairaut differential equation is, y = xy’ + (y’)2 ……(1)   Differentiate the above equation with...

Q: f(x) = x4 - 2x3 + x2 a. Use the Leading Coefficient Test to determine the graph’s end behavior.b. Fi...

A: f(x) = x4 - 2x3 + x2 a. Use the Leading Coefficient Test to determine the graph’s end behavior.b. Fi...

Q: Find distance the poinl- the between Cziz16) f * +y=0, J - Z =1 the line

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Q: You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller ...

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Q: Use the comparison test to determine whether the series ∞ ∑      (2+sin^(3)(n+1))/(2^(n)+n^2) conver...

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Q: Show that a rectangular box of given volume and minimum surface area is a cube.

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Q: Find an equation of the tangent plane to the surface g(x, y) = x2 + y2, at the given point (1, −1, 2...

A: We have given the surface; g(x, y) = x2 + y2 and the point (1, −1, 2)

Q: Find the one-sided limit (if it exists).

A: We first factor the denominator  

Q: Use a convergence test of your choice to determine whether the following series converge.

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Q: 2:-How many hits afe required to represent the Bollowsing decimal lumbers ? 0) 17 b) 49 c) l14 ) 205

A: a. 

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function : f(x) =...

A: We compare  f(x) = 3x2 - 12x + 1 with  f(x) = ax2 +bx + c  So, a=3, b=-12, c=1   

Q: State the name of the property illustrated as 11 . (7 + 4) = 11 . 7 + 11 . 4

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Q: The volume, V, of a rectangular solid with length l, width w, and height h is given by the formula V...

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Q: Find ∫(sec x/ tan2 x) dx.

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Q: Gradient fields Find the gradient field F = ∇φ for the potentialfunction φ. Sketch a few level curve...

A: Given potential function We need to find the gradient field.

Q: Help my solve the inequalities for this equation... Problem #1  l 1 - 4x l -7  </=(but equal to) ...

A: Absolute rules: If |x| < a, then –a < x < a. If |x| ≤ a, then –a ≤ x ≤ a.   (b) The given i...

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Q: write the general solution of the differential equation

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Q: How do you find the fifth derivative of a function?

A: To find the derivative we differentiate the function once.  To find the second derivative we differe...

Q: In this problem we assume that fish are caught at a constant rate h independent of the size of the f...

A: We have given the differential equation;  

Q: Find all zeros of f(x) = x3 + 5x2 - 8x + 2.

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Q: Write each number in scientific notation:a. 5,210,000,000   b. -0.00000006893.

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Q: Find the distance between the given parallel planes. 6z = 4y − 4x,    9z = 2 − 6x + 6y

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Q: Evaluate the limit.

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Q: Evaluate

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Q: Write the formula for Newton’s method and use the given initialapproximation to compute the approxim...

A: We first find f'(x)  

Q: Use reference angles to find the exact value of the expression sin(-240°). Do not use a calculator.

A: Note that -240° is in the second quadrant. There sin is positive.  To find reference angle of -240° ...

Q: a1=2    a2=2/4    a3=2/9    a4=2/16 what is a5? what is the nth term in the sequence?

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Q: Consider the following problem: A farmer with 750 ft offencing wants to enclose a rectangular area a...

A: Given: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into f...

Q: Determine whether the statement is true or false. If the statement is false, make the necessary chan...

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Q: Trigonometric integrals Evaluate the following integrals.

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Q: Find the derivative of the function f(t) = t 3/2 log2 √( t + 1)

A: Here, This can be written as By factoring out the constant term  

Q: 7- Please I want answer of this question. Thanks   Note: Z = 3

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Q: Show that x – P VB + (d - x)* g(x) is a decreasing function of x.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.