sketch the region described by the following cylindricalcoordinates in three-dimensional space. r = θ

Q: find an equation for the plane through pointsP, Q, and R. P(1, -1, 2), Q(2, 1, 3), R(-1, 2, -1)

A:

Q: Use the given conditions to write an equation for the line in point-slope form and slope-intercept f...

A:

Q: Write the repeating decimal first as a geometric series and then as a fraction (a ratio of two integ...

A: We separate the decimals so that we can express a part of it as geometric series.  

Q: 19-22 - Properties of Real Numbers Rewrite the expression using the given property of real numbers. ...

A: To rewrite the expression using the given property of real numbers. 19) Commutative property of addi...

Q: Evaluate the limit.

A: Given limit:

Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx  

Q: A rectangular storage container with an open top is to havea volume of 10 m 3 . The length of its ba...

A:

Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule to approximate the given ...

A: Given 

Q: Use the simpson's Rule to estimate the integral below. Be sure to show your function values, and a t...

A: To determine: The value of the given integral using Simpson’s rule with 4 subintervals.

Q: The domain of the function f shown in the figure is −6 ≤ x ≤ 6.                     (a) Complete the...

A: a) If f(x) is even then, the graph will be symmetric about the y-axis.  So we reflect the curve over...

Q: Use the Comparison Theorem to determine whetherthe integral is convergent or divergent.

A:

Q: If f(x) = 4x2 - 2x + 7, find and simplify.

A: First we find f(x+h)  

Q: How can the Approaching of  a Limit from One Side be done?

A: In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x a...

Q: Let logb 2 = A and logb 3 = C. Write the expression logb √(3/16) in terms of A and C,

A: Given :  

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

A: We will find this limit by substitution   

Q: Match the equation 4x2 − y2 = 4 with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and...

A: We first write the equation in the standard form So this is a hyperbola. (Horizontal) With center a...

Q: Remainders Find the remainder Rn for the nth-order Taylor polynomial centered at a for the given fun...

A:

Q: Solve: -2x - 4 = x + 5.

A: We subtract x from both sides  

Q: Find the absolute extrema of the function (if any exist) on each interval                       f(x)...

A:

Q: 11-16 - nth Term of an Arithmetic Sequence Find the nth term of the arithmetic sequence with given f...

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re...

Q: A customer in a coffee shop purchases a blend of two coffees: Kenyan, costing $3.50 a pound, and Sri...

A:

Q: Use the Trapezoid Rule to estimate the integral below. Be sure to show your function values, and a t...

A: To determine: The value of the given integral using the trapezoidal rule with 4 subintervals.  

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = (6 − x)...

A:

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = xn, x = 1...

A: Given ,  

Q: Curvature Find the unit tangent vector T and the curvature k for the following parameterized curve. ...

A:

Q: Consider the function below

A:

Q: Calculus Question

A: We write the exponent 4, as a product of two squares Then we use the Pythagorean identity Then dis...

Q: For the position function s(t) = - 16t + 108t, complete the following table with the appropriate ave...

A: Given data:     The expression for the position function is: s(t)=-16t2+108t.   Substitute 1 for in ...

Q: What does it mean for a function to have a local extreme value on its domain? An absolute extreme va...

A: For a function defined in a domain and having a particular range has a local extreme value. This val...

Q: The number of apples produced by each tree in an apple orchard depends on how densely the trees are ...

A: We have to maximize A(n) = n(900 - 9n) We find dA/dn    

Q: Convert the following expression to the indicated base. a1>log10 a using base 10, for a 7 0 and a...

A:

Q: fc (y+z) dx (x+z)dy+ y2 dz, C consists of line segments from (0,0,0) to  (1,0,1)  and  (1,0,1)  to (...

A:

Q: evaluate the given integral.

A: Then we use substitution  

Q: determine whether the piecewise-defined function is differentiable at x = 0.

A: We first find the Right and left-hand limit of f'(x)  

Q: Integration techniques Use the methods introduced evaluate the following integrals.

A:

Q: Show by induction that if (n) is a positive integer, then ((n^3) - n) is divisible by 6.

A: Given statement is

Q: Suppose the functions ƒ(x) and g(x) are defined for all x and thatlimx→0 ƒ(x) = 1/2 and limx→0 g(x) ...

A:  

Q: Write an algebraic expression that is equivalent to the given expression. cos( arcsin() x- h |

A:

Q: Find the centroid of the solid bounded by the xy-plane, the cylinder x 2 + y 2 = R2, and the plane x...

A:

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A:  A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|  

Q: Use an identity to solve the equation sin (x + π/4) + sin (x - π/4) = 1 on the interval [0, 2π).

A: We will use sin(A+B)=sinAcosB+cosAsinB and sin(A-B)=sinAcosB-cosAsinB    

Q: Complete the following statement. If dy/dx is small, then smallchanges in x will result in relativel...

A:

Q: find the work done by F over the curve in thedirection of increasing t. F = 6z i + y2j + 12x kr(t) =...

A:

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.