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Q: Evaluate the following limits: 5/(e^x)+7 as x approaches infinity 5/(e^x)+7 as x approaches negative...

A: Given:

Q: Change from rectangular to cylindrical coordinates. (Let r 2 0 and 0 s 0 s 2t.) (a) (4, -4, 5) (42, ...

A: a). Given rectangular coordinates are

Q: The position of an object in circular motion is modeled by the given parametric equations. Describe ...

A: The two parametric equations are, x=2sint and y=2costFor calculating the radius of the circle, we us...

Q: Why is 00 an indeterminate form while 10 is not? Explain this in a few steps.(a) Recall that a 0 0 i...

A: To discuss which ratios are indeterminates (and which are not).

Q: Differentiate the function F(t) = (ln t)2 sin t

A: Given function is,

Q: What does the nth term test determine for the summation of (e^n)/(e^n+n) from 0 to infinity?

A: We are given the expression,

Q: An underground gasoline storage tank is leaking. The tank currently contains 600 gallons of gasoline...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Find an equation of the tangent line to the curve at the given point. y = 5ex cos(x), (0, 5)

A: To find the equation of the tangent line at the point (0, 5) to the curve given below.

Q: see attachment

A: Part(a):Given:

Q: Consider the limit: lim x→0csc(6x)sin(7x).(a) What is the form of the limit?(b) Based on the form, w...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: see attachment

A: To determine the value of x.

Q: How do you get the derivative of (6-18x^2)/((1+3x^2)^2)?

A: Given function is

Q: Find a formula for n in terms of m where: n is a length in feet and m is the length in inches.Note t...

A: We have to find a formula for n in terms of m where n is a length in feet and m is the length in inc...

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval.x = 3sin(t)...

A: To find: The motion of particle.The expression is rewritten as,

Q: A silo (base not included) is to be constructed in the form of a cylider surmounted by a hemisphere....

A: Click to see the answer

Q: let f(x)=1/2ln(1+x/1-x). compute the inverse function f-1 (x) and find its domain and range.

A: Find the inverse of the function and find its domain and range

Q: 2 Find the volume of the ellipsoid 2y 7z 16

A: Volume of the ellipsoid for the equation,

Q: Consider the following.x = sin(t)y = csc(t)0 < t < π/2(a) Eliminate the parameter to find a Ca...

A: It is given that,

Q: see attachment

A: Factor out 2.

Q: see attachment

A: For a function of the form y=A sin(B(x+C))+D, amplitude is A, period is 2pi/B,phase shift is C.So we...

Q: The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10 fe...

A: To estimate the height using numerical integration

Q: The world's output of primary energy (petroleum, natural gas, coal, hydroelectricity, and nuclear el...

A: It is increasing at the rate of 2.4% annually. So 0.024 every year.growth rate= (1+0.024)=1.024 per ...

Q: Calculus Question

A: Given,

Q: Can you help with this problem step by step?

A: Given,

Q: see attachment

A: Graph the solution to the system of inequalities.

Q: Find the linear approximation to the function. x2 f(x + Δx) ≈ Evaluate it at the given va...

A: Click to see the answer

Q: Find the particular solution of the differential equation dy/dx+ycos(x)=4cos(x) satisfying the initi...

A: Given differential equation is,

Q: find the critical points:

A: Given function is and the interval isThe critical points of a function are obtained when the first ...

Q: Find ∂z / ∂v using the chain rule if z = sin(x/y), x = ln(u), and y = v. Put the answer in terms of ...

A: Firstly, we find partial derivative of z with respect to x and y, partial derivative of x with respe...

Q: If xy + ey = e, find the value of yn at the point where x = 0.

A: xy + ey = eWhen x = 0, ey = e = e1Hence, y = 1

Q: indefinite integral of x3 dx

A: Click to see the answer

Q: Calculate dy/dx Simplify your answer. y = x3(8 − x2) dy/dx=

A: Product rule:

Q: 3.4 Can you show me the steps to solve the problem? Directions: Find the limit or show that it does ...

A: Divide the expression by the highest power of the denominator.

Q: The number of children under 18 living in households headed by a grandparent can be modeled as p(t) ...

A: Consider the given information:

Q: 10 5 0 -1 -10 Identify the graphs A (blue), B( red) and C (green) as the graphs of a function and it...

A: A(blue) is the graph of the functionB(red) is the graph of the function's first derivativeC(green) i...

Q: 51 and 52 Find dy/de and d2y/dz2. For which values of t is the parametric curve concave upward? 51. ...

A: 52. The given parametric curve are

Q: Height At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate ...

A: Let the altitude be denoted by h, Diameter by d, Radius by rIt is known that d=2rAs per given criter...

Q: Write the equation in spherical coordinates. 2x2 - 3х + 2y2+ 22? (a) = 0 3p(p sin(p)cos (0)) 2 2х + ...

A: Consider the following spherical coordinates.

Q: Use the Quotient Rule to differentiate the function f(x) = (tan(x) − 1)/(sec(x) Simplify the expre...

A: Given:

Q: Find positive numbers x and y satisfying the equation xy=15 such that the sum 3x+y is as small as po...

A: Click to see the answer

Q: I need help with question 39 in Section 4.1, page 284, of the James Stewart Calculus Eighth Edition ...

A: At first let us find the derivative of the function:

Q: Find the derivative of the vector function ta x (b tc), where r(t) = (-1,1,-2) а %3 (-2,3, -1), ь 3 ...

A: Given vector function is,

Q: Can you help me with this problem step by step?

A: Consider the function f(t) = 12t - t3 in the interval [-3, ∞).

Q: Find the radian measures that correspond to the degree measures 260° and −155°. (I really just need ...

A: Click to see the answer

Q: For the pair of functions, find the derivative of the composite function c(x(t)) in terms of one inp...

A: Click to see the answer

Q: The average length of the outer ear for men can be modeled as f(x)0.89 0.495 In x inches a s 70.T wh...

A: Find f (x(15)) as follows.

Q: The amount of caffeine in the bloodstream decreases by 26% every hour. A cup of coffee contains 94...

A: Hi, your question has six sub questions. We answer upto three sub questions as per our policy. Pleas...

Q: Evaluate the integral dx/2sqr(x+3)+x

A: Given that

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one inpu...

A: Given,

Q: Write a derivative formula for the function. f(x) = 8x√(7x+2) +91

A: Given,