Find the sum of the first 100 terms of the arithmetic sequence: 1, 3, 5, 7, ...........

Q: Use a change of variables or Table toevaluate the following definite integrals.

A: the given definite integral is: ∫132x2x+4dx we have to evaluate the given definite integral by using...

Q: In Exercises 1-20, apply the Ratio Test to determine convergence or divergence, or state that the Ra...

A: Consider the provided series, ∑n=1∞10n2n2 Apply the Ratio Test to determine convergence or divergenc...

Q: Trigonometric integrals Evaluate the following integrals. ∫sin2 x cos2 x dx

A: We have to evaluate the integral: ∫sin2x cos2x dx Since we know the identity, 2sinx cosx=sin2x There...

Q: Evaluate the following integrals. 1) integral of (3r/(1-r)^1/2))dr 2) integral of ((2+5y)^1/2)dy

A: 1) integral of (3r/(1-r)^1/2))dr

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions as : n...

A: the given conditions are: n=4; 2(with multiplicity 2) and 3i are zeroes, f(0)=36 we have to find an ...

Q: Find dy/dx in following. )y=x' costx + xsin?x -2

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

Q: In Exercises 43-62, determine convergence or divergence using anymethod covered in the text so far.

A: Given:∑n=1∞ sin nn2

Q: Problem 2. Let f: (0, 7 /2) →R be defined by f(x)=cos(x)x" . Then f'(1) is (A) cos(1) – sin(1) (B) c...

A: It is given that fx=cosxxx. Obtain the derivative of fx=cosxxx: f'x=-sinxxx+xxlnx+1cosx=-xxsinx+xxco...

Q: 8. If the radius and height of a cone grow 1.8% and 2.0% from its original value, respectively, calc...

A: The volume of cone(V), with radius (r) and height (h), is given by, V=13πr2h Substitute h=2r to get ...

Q: Find the critical numbers of f, if any, (a) find the open intervals on which the function is increas...

A: Given that f(x) = (x2 − 2x + 1)/(x + 1) We need to: 1) find the intervals in which function is incre...

Q: Determine the following indefinite integral.

A: To calculate the given integral

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2/3(...

A: we have to find the intervals on which f(x) is increasing and the intervals on which f(x) is decreas...

Q: A fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water. At what rat...

A: Given: A fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water and t...

Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.  

Q: Eliminate the parameter and obtain the standard form of the rectangular equation.           Circle: ...

A:

Q: 2. Provide the differential for a* = y*. A. dy = a*-xda + (a* In a – y* In y)dx B. y*-dy = a*-1xda +...

A: The given equation is ax=yx        . To find The differential equation for the equation. Solution: T...

Q: Solve the following differential equation Y^2 + x^2p^2 - 2xyp=4/p^2

A:

Q: A TV set was bought for $26,250 including  5% VAT [Value added tax]. Find the original price of the ...

A: GIVEN 5% VAT

Q: Fill in the blank/s: The principle of mathematical __________ states that a statement involving posi...

A: Solution: Consider the given fill in the blank: The principle of mathematical induction states that ...

Q: Use the power-reducing formulas to rewrite sin6 x as an equivalent expression that does not contain ...

A: Given: y=sin6x for reducing power, we simplify given expression so, y=sin6x=sin3x2                  ...

Q: Determine whether the following series converge. Justify your answers.

A: Given: ∑k=1∞ 7k+11k11k Determine whether the following series converge. Now rewrite the given series...

Q: Problem 15. Let f be a continuous function on the closed interval [0, 1]. Which of the following sta...

A:

Q: Evaluate the integral.

A: Consider the given integration as ∫13381+x2dx  

Q: If f(x) = 3x + 7, find

A: we have been given the function f(x) = 3x + 7  we have to use the formula  f(a+h)-f(a)h          (1)...

Q: Comparing distances Suppose two cars started at the same time and place (t = 0 and s = 0). The veloc...

A: Given: Two cars started at the same time and place (t = 0 and s = 0). The velocity of car A (in mi/h...

Q: Problem 15. Let f be a continuous function on the closed interval [0, 1]. Which of the following sta...

A: Let us check one by one. I. ∫01fx2dx=∫01fx2dx Let us consider the function f(x) = x + 1. ⇒fx2=x2+1 a...

Q: A kite flies at a height of 30 feet when 65 feet of string is out. If the string is in a straight li...

A: Given: A kite flies at a height of 30 feet when 65 feet of string is out. The figure gives the clear...

Q: Give a geometric description of the following sets of points. x2 - 2x + y2 + 6y + z2 + 10 = 0

A:

Q: find the value of y when x=1

A: Given: dydx=x2+x-5 and y=53 when x=2. Now, given equation dydx=x2+x-5 can be written as: dydx=x2+x-5...

Q: The answer to question (i) and (ii) is (i) - 12(3-2x) ^-2 x 2 (ii) 0 or 3 How do I show the working ...

A: Given: A curve has an equation y=123-2x (i) To find dydx, differentiate both sides of the given curv...

Q: A TV set was bought for $26,250 including  5% VAT [Value added tax]. Find the original price of the ...

A:

Q: Fill in the blank so that the resulting statement is true.

A: Given inequality, x-3y<62x+3y≥-6

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.