Consider a curve represented by the parametric equations x = f(t) and             y = g(t). When does the graph have horizontal tangent lines? Vertical tangent lines?

Q: Determine whether each of the following series is convergent or divergent. Indicatetest used.

A: Explanation of the solution is given below...

Q: Walking on a surface Consider the following surfaces specified in the form z = ƒ(x, y) and the orien...

A: Given: z = 4x2 - y2+ 1, C: x=cos t, y=sin t; 0 ≤ t ≤ 2π

Q: The median waiting time (in minutes) for people waiting for service in a convenience store is given ...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Find local extrema and saddle points of the function f(x, y) = y^2 - 3y cos x , -1 ≤ x ≤ 7

A: Given: fx,y=y2-3ycosx,  -1≤x≤7

Q: Given, f(x) = 2x4 + 2x3 - 22x2 - 18x + 36, shown (see attached) incomplete graphs of given polynomia...

A:

Q: Find the volume of the solid generated by revolving the region under the curve y=2x-x^2 about the x-...

A: Given y=2x-x2

Q: Solve the exponential equation e5x-3 - 2 = 10,476. Express the solution set in terms of natural loga...

A: the given exponential equation is e5x-3-2=10476 we have to solve the given exponential equation. we ...

Q: Show that the equation x2 - 4y2 + 2x + 8y - 7 = 0 represents a hyperbola. Find its center, asymptote...

A: Given: x2-4y2+2x+8y-7=0 first we converting given equation in standard form so, x2-4y2+2x+8y-7=0x2+2...

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it converges...

A: Given, ∫51010xdx This is improper integral, So we can write it as, ∫51010xdx=limt→0∫t510xdx∫51010xdx...

Q: 9x* - 6x - 36y + 37 = 0 (x, v) = ( | center y) = focus (x, y) = (smaller x-value or only focus) (x, ...

A: 9x2-6x-36y+37=0 On simplification, we get ⇒36y=9x2-6x+37⇒36y=9x2-23x+37⇒36y=9x2-23x+19+37-1⇒36y=9x-1...

Q: 15-18 - Graphing Linear Functions For the given linear func- tion, make a table of values and sketch...

A: Answer to question 15.   The function is, fx=2x-5   Plot the table for different x and y values. ...

Q: Give precise definitions of the following statements. limx→2- ƒ(x) = 5

A: The given statement (limit) is:  limx→2-fx=5 The precise definition of the given statement (limit) i...

Q: Derive the identity using the identities listed in this section.

A: identities:1)  cos2θ = 1-2sin2θ2) sin2θ = 2.sinθ.cosθsin2xcos2x = 1-cos4x8

Q: Compute the limit:lim (1+3x)^(-5/x)x→0

A: We have to evaluate the given limit.

Q: Write the equation in its equivalent exponential form: log5125 = y

A: Given:log5 125 =yFormula:loga ap=p

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then ...

A:

Q: Solve the linear equation: (x + 1)/3 = 5 - (x + 2)/7.

A: Given the linear equation, x+13=5-x+27

Q: Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x...

A: we have to write an equation in standard form of the parabola that has the same shape as the graph o...

Q: Average and marginal cost Consider the following cost functions.a. Find the average cost and margina...

A: a. Consider the given cost function, Cx=-0.01x2+40x+100 the marginal cost function is the first deri...

Q: Write the standard form of the equation of the circle with center (0, 0) and radius 2. Graph the cir...

A: Given: center=0,0radius=2  

Q: By your cell phone contract you pay a monthly fee plus some money for each minute you use the phone ...

A: Given,  Cell phone contract: You pay a monthly fee plus some money for each minute you use the phone...

Q: Find the exact value of the trigonometric function tan(5π/4). Do not use a calculator.

A:

Q: Solve the exponential equation 3x = 81 by expressing each side as a power of the same base and then ...

A: Given exponential equation is 3x=81   ....1

Q: Use a graphing utility to determine the first term that is less than 0.0001 in each of the convergen...

A: Given that, The series ∑n=1∞1n(n+1) and ∑n=1∞18n We need 1n(n+1)<0.0001 Now we have to solve it f...

Q: Solve the equation for B: 51/sin 75° = 71/sin B by using the cross-products principle to clear fract...

A: Given: 51sin75∘=71sinB                                          ..1 we solve equation1, by using cro...

Q: How close to - 3 do we have to take so that

A: Suppose for some x,                             1(x+3)4> 10,000  

Q: Determine whether each of the following series is convergent or divergent. Indicatetest used.

A:

Q: Write the equation in its equivalent logarithmic form: b3 = 27

A: Given : b3 = 27

Q: Fill in the blank/s: The graph of y = f(-x) is the graph of y = f(x)reflected about the ...............

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Radioactive decay The mass of radioactive material in a sample has decreased by 30% since the decay ...

A: Let C(t) be the mass of radioactive material in a sample of t years after the initial mass C0. Then,...

Q: A 3-foot kid wanted to play with his shadows in the middle of the night, with a flashlight as the on...

A: Given: Height of kid : 3 feet Distance of flashlight from wall : 5 feet Speed of kid towards the wal...

Q: Find an equation of the plane that contains all the points that are equidistant from the given point...

A:

Q: In a class of 50 students, 29 are Democrats, 11 are business majors, and 5 of the business majors ar...

A: Concept:   The calculus helps in understanding the changes between values that are related by a func...

Q: Answer this question.

A: the given graph is  a) We have to complete the speed-time graph First, for   0 - 25 sec Blue line ...

Q: Find the product and write the result in standard form. (8 - 4i)(-3 + 9i)

A: the given expression is: 8-4i-3+9i we have to find the product and write the result in standard form...

Q: Determine whether the series converges absolutely or conditionally, or diverges.

A: Given: ∑n=1∞ -1nn! To determine: Given series is convergent (absolutely or conditionally) or diverge...

Q: 51. (a) 4 = -cı (b) c1(t) = 8e(-2/5)t g/L

A: (a) Given information: dc1dt=-25c It is first order seprable ODE    

Q: Prove that f(x)=log(x)-x^2 +1 has exactly two roots namely x=1 and x=0.45

A: Function: f(x)=log(x)-x2+1 If it has two roots x=1 and x=0.45 then f(1)=0 and f(0.45)=0. If both of ...

Q: A couple needs $60,000 as a down payment for a home. If they invest the $45,000 they have at 4% comp...

A: Given: The initial investment is $45,000, rate of interest is 4% means 0.04, interest rate is compou...