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Q: Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point...

A: Consider the given curves and points.

Q: 7. According to a simplified economic model, the purchasing power of 1 dollar in the 2000t is equal ...

A: 2000+t=2020So, 20 years.

Q: Find the Taylor polynomial of degree 2 centered at (1, 2) for thefunction f(x, y) = 1/(xy)

A: Definition:

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0 < 0 < 2n, and 0 s p n.) (0, 2 3, 2) ...

A: Formula for the converting rectangular coordinates to spherical coordinates.

Q: 4. Use the properties of logarith ms to rewrite each expression as the logarithm of a single express...

A: We know that,

Q: FInd the diemsions of a rectangular box, open at the top, having volume 727cm^3, and requiring the l...

A: Let the length, breadth and height of the box be denoted by a, b and h respectively, thenV=a × b × h...

Q: solve the equation 2cos(x+ 7π/4)=√3 giving the exact solution which lie in [0,2π)

A: Divide by 2.

Q: Finding a Polynomial Find a third degree polynomia p(x) that is tangent to the line y = 14x - 13 at ...

A: Let p(x) = ax^3 + bx^2 + cx + dThis passes through (1,1) and (-1,-3) . For (1,1), x=1 and y=1. For ...

Q: If the figure is the graph of the derivative f', answer the following: Where do points the points of...

A: Point of inflection occur at f"=0That is (f')'=0Means we have to find where the graph of f' takes tu...

Q: A piece of wire of length 63 is cut, and the resulting tow pieces are formed to make a circle and a ...

A: The total length of the wire is 63.Let x be the length of the wire cut for the circle.Then, 63-x is ...

Q: for this problem in the answer it says, cos^-1 (1/2)= pi/3,-pi/3. Why is that? Why did they go count...

A: According to question

Q: Match the blue graph of each function to the black graph of its derivative by writing the letter (A,...

A: Consider the first function:

Q: A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let ...

A: To find the number of units that should be produced at each location to minimize the cost.

Q: find the derivative 1).f(x)=X^3(X^4/3-1) ...

A: 1)

Q: f(x)-f(a) a. Use the definition mtan = lim to find the slope of the line tangent to the graph of f a...

A: Part (a) P(-3, 2) = [a, f(a)]Hence, a = -3, f(a) = 2Please see the whiteboard for the calculation of...

Q: Express the given quantity as a single logarithm. 2)2 In(x 2)7In x - In(x2 +

A: Let the given expression is:

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

A: Given,

Q: The population (in millions) of the United States between 1970 and 2010 can be modeled as p(x) = 20...

A: Consider the given information:

Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) wit...

A: The position vector,

Q: 5 5 find sec(0) 12 and tan(e) 13 If sin(0)

A: Given,

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: Linear Approximate the change in the lateral surface area (excluding the area of the base) of a righ...

A: We have

Q: Given that the graph of f passes through the point (1,6) and that the slope of its tangent at (x, f(...

A: Given that the slope of the tangent at (x, f(x)) is 2x + 1.That is,

Q: Exercise 3: Find A and B given that the derivative f'(r) is everywhere continuous, and Aa2 Bx 2, x<2...

A: The function f(x) whose derivative is everywhere continuous is given by,

Q: f(x)=(4x^2)/[(x^2)−4]. Calculate the first derivative of f. Find the critical numbers of f, where i...

A: The given function is,

Q: Sketch the graph of a functionf having the following characteristics f(2) f(4) 0 f(x)0 if x > 3 f(3)...

A: First point represents the the x-intercepts. Second and fourth point is telling that the graph is in...

Q: Find the derivative of the function. f(x) = (2x − 3)4(x2 + x + 1)5

A: Given function is

Q: dy Given the equation below, find 36542yys = 41 dy da

A: We are given,

Q: Logarithmic Differentiation of (ln x)^x^2

A: Given expression

Q: -x2 The demand function for a product is p D(x) = 300e200 revenue. Show all of your work to prove it...

A: We know that Revenue function is given by

Q: An investment of $9,000 earns interest at an annual rate of 6.5% compounded continuously. Complete A...

A: Use the following formula,

Q: Does the series ∞ ∑(cos(πn))/n(squareroot(n)) n=1 converge absolutely, converge conditionally, or...

A: Consider the given series,

Q: 7 If sin(0) 7 find sec(e) 24 and tan(0) 25

A: From the given information:

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: h(t) f(x, y), where f is differentiable, ax = g(t), and y Suppose z - 4, h' (6) 6, f2(8, If g(6) 8, ...

A: We are given that z = f(x, y), where f is differentiable, x = g(t), and y = h(t).

Q: Find dy/dx.x = t sin(t)y = t2 + 3t

A: Click to see the answer

Q: Express -x 2dx as aumit X eSS OF ngnt -hard Riemann Sums las the definition Of the indlefmite T cuva...

A: Given integral

Q: 4. Find the area that lies inside the curve r = 4 cos and outside the curve r = 2.

A: Given, curves are

Q: I can't find the tangential component of the acceleration

A: The given position vector is,

Q: Use logarithmic differentiation to find the derivative of the following function: y = (x - 1 / x4 + ...

A: Apply ln on both sides and simplify using properties of logarithm.

Q: 10 0 x 2 et where x thousand lipsticks were sold per week at a price of p dollars each. At what pric...

A: Given:

Q: I am very confused on these two problems and I have homework due in 30 minutes.

A: Both problems concern finding deriviatives of functions ,using standard rules of differentiation

Q: I need help with question 21 in Section 3.11, page 264, of the James Stewart Calculus Eighth Edition...

A: Given,

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Click to see the answer

Q: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a spher...

A: Let r be the radius of the cylinder and h be the height of the cylinderR is the radius of the sphere...

Q: Optimization: A family wants to build a fence in their backyard for their dogs. If they can only aff...

A: Click to see the answer

Q: Find an equation of the tangent line to the astroid at the (3√3, 1). x2/3 + y2/3 = 4

A: Given an astroid equation find the equation of tangent at a point.

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: 49. Let f(t) be the temperature at time t where you live and suppose that at time t 3 you feel uncom...

A: a) f'(3)=2, f"(3)=4f'(3) > 0 , so the temperature f(t) is increasing at x=3f"(3)>0 implies at...

Q: Consider the following.x = 1 + t2y = t2 + t3 (a) Find the following.(dy)/(dx) = (d^2y)/(dx^2) = (b) ...

A: Click to see the answer