In Problem evaluate the improper integrals that converge.

Q: Linear Equations The given equation is either linear or equivalent to a linear equation. Solve the e...

A: Since you have posted multiple questions we solve the first three questions for you To get the solut...

Q: Set w(r, y) = cos(xy) where x = t² and y = el-8t, then dw is dt Select one: a. -2ysin(xy)t^1+8xsin(x...

A: to find the value dw/dt                   dwdt=dwdx.dxdt+dwdy.dydt                     (1)

Q: Find the limits

A: Consider the given function, limx→∞x2+25-x2-1 rationalize the function, limx→∞x2+25-x2-1=limx→∞x2+25...

Q: b. Determine the length of radius of the circular ripple after 3 seconds. A rock is thrown into a la...

A: Given that a rock thrown into a lake creates a circular ripples that gets larger over time , where a...

Q: decide if the given statement is true or false,and give a brief justification for your answer.If true...

A: in homogenous equation  x′(t)= A(t)x(t)+b(t), b(t) = 0 so, the general  solution to this equation wi...

Q: Write an equation involving a, b, and c based on the following description:When the value of x in y ...

A: It is given that the value of x in y = ax2 + bx + c is 4, the value of y is 1682.

Q: Use Stoke’s Theorem to evaluate the line integral ∮C(x+z)dx +(x−y)dy +xdz. The curve C is the ellips...

A:

Q: Use the definition of the derivativeand the trigonometric identity

A: Given function is fx=cosx

Q: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1+ 2y2 ,1...

A: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1+ 2y2 ,1...

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = (x3 + ( y/2))2/3

A: Given: fx,y=x3+y223 To Find: δfδx and δfδy. Concept: a. fgx'=f'gx·g'xb. ddxxn=nxn-1

Q: Evaluate the limit.

A: limt→∞t43+t134t23+12

Q: e or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the ...

A: Given the graph of f: To sketch the graph of f'

Q: Solve  (D^2 - 9)y = e^(4x)

A:

Q: Determine whether Rolle’s Theorem applies to the following function on the given interval. If so, fi...

A: Role's theorem: Let f be a continuous function on a, b and differentiable on a,b. If fa=fb then ther...

Q: 5x - 4 e Find the equation of the tangent line to the graph of f(x) = at (0, - 2). 5x +2 The equatio...

A: Solution: The objective is to find the tangent line to the given function

Q: Compute the discriminant of 4x2 - 8x + 1 = 0. What does the discriminant indicate about the number a...

A: Given: 4x2-8x+1=0

Q: Use a calculator to find the value of the acute angle cos θ = 0.4112 in radians, rounded to three de...

A: Since, we have to find the value of the acute angle cosθ=0.4112 in radians rounded to three decimal ...

Q: Fill in the blanks? If n is a counting number, bn, read …….., indicates that there are n factors of ...

A:

Q: Complete the square and write the given equation x2 + y2 - 6y - 7 = 0 in standard form. Then give th...

A: Given equation x2+y2-6x-7=0 Solve for completing the square x2+y2-6x-7+9=0+9x-32+y-02=42 Comparing t...

Q: a. Find the open intervals on which the function is increasing and those on which it is decreasing. ...

A:

Q: integrate?

A: To find the integration.

Q: In 2000, the population of Greece was 10,600,000, with projections of a population decrease of 28,00...

A: Population of Greece in 2000 =  10600000Population of Greece in 2001 after 1 year = 10600000 - 28000...

Q: - Local Extrema Graph the polynomial in the given viewing rectangle. Find the coordinates of all loc...

A: (55) Consider the given function as y=-x2+8x

Q: Use l’Hôpital’s rule to find the limits

A: To evaluate the given limits lim x→0sin3x-3x+x2sinxsin2x Solution: Since we know that, lim α→0sinαα=...

Q: Find the derivative of the function. y = x sec k x

A: The function is given as , y=x seckx. To find the derivative for the given function. Solution: The f...

Q: (a) Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1&l...

A: (a) First we sketch the curve Let x = a is any point of x – axis, such that the line x = a bisects ...

Q: What is defined as the mathematical study of continuous change?

A:

Q: The exponential growth models, A = 33.1e0.009t (Canada) and A = 28.2e0.034t (Uganda) describe the po...

A: Determine whether the statement "The models indicate that in 2013, Uganda’s population will exceed C...

Q: Assume ƒ is an odd function and that both ƒ and g are one-to-one. Use the (incomplete) graph of ƒ an...

A:

Q: Evaluate the integral by interpreting it in terms of areas: xp |xJ

A: The given integral is ∫-22xdx. The limit of x lies between -2 and 2. The integrand is the function x...

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A: To Evaluate: limx→0+sinx1-xx Concept: (a). L-Hopital's Rule:If limx→afxgx=00 or limx→afxgx=±∞±∞then,...

Q: 7-8 - Yes or No? If No, give a reason. 7. (a) Is the expression () equal to ? (b) Is there a differe...

A: Since you have asked multiple question, we will solve the first question for you. If you want any sp...

Q: a) If the consumption function isC = 50 + 2√Ycalculate MPC and MPS when Y = 36 and give an interpret...

A: According to the guidelines only one question will be answered please upload other question separate...

Q: Find an equation of the tangent line to the graph of the function at the given point, (a) use a grap...

A: consider the given function, fx=2x34 to find the equation of the tangent line first find the slope o...

Q: simplify x + 2 61. 62. x + 2 -E-

A: (61) Consider the given expression as 1+1x+21-1x+2

Q: Find the derivative of the trigonometric function f(x)=sin2x using the limit definition.

A:

Q: Find the derivative of the function.

A: Given: y=∫2x3x+1sint4dt

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.