Question

find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d2y/dx2 at this point

1. x = 2 cos t, y = 2 sin t, t = pai/4

2. x = sin 2pai t, y = cos 2pai t ,t=1/6

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4, ...

A: Click to see the answer

Q: Express in terms of sums and differences of logarithms

A: According to the given information it is required to write the expression in terms of sum and differ...

Q: find the component form of the vector. The sum of AB and CD, where A = (1, -1), B = (2, 0), C = (-1,...

A: Given that A = (1, -1), B = (2, 0), C = (-1, 3), and D = (-2, 2)We have to find AB + CD. 

Q: Find equations for the sphere whose centers and radii are given in center(1,2,3) radius sqrt(14)

A: To determine the equation of a sphere.

Q: Find the volume of the solid that results when the shaded region is revolved around the indicated ax...

A: Given a solid that resulted when the shaded region is revolved around the indicated axis. 

Q: Find the rules for the composite functions f ∘ g and g ∘ f.   f(x)=square root of (x+9) and g(x)= 1...

A: fog means f(g(x))We plug g(x)=1/(x-9) inside f(x).Then replace x in f(x) by 1/(x-9) to find f(1/(x-9...

Q: In the function:  f(x)= (7x+B)/(4x+b) , with 7b>4B At which x does the function reach its local m...

A: According to the given information it is required to calculate at which x does the function reach it...

Q: #9

A: Given:Initially water tank holds 300 gallons of water.Rate at which the pure water is pumped into th...

Q: Find the limit of the trigonometric function. (If an answer does not exist, enter DNE.) lim cos(60) ...

A: We need to find the limit of the given trigonometric function.

Q: What happens if you add a finite number of terms to a convergent series? A divergent series? What ha...

A: As there are multiple parts to the question, we will address the par related to divergent series fir...

Q: Exercises 49–50 give equations for ellipses and tell how many units up or down and to the right or l...

A: Note: We’ll answer the 49th question since we answer only one question at a time. Please submit a ne...

Q: Find the values of the variables. 1 1 x 4 1 13 3 3 z %3D 4 2 х IL || ||

A: Given:

Q: What is a parabola? What are the Cartesian equations for parabo-las whose vertices lie at the origin...

A: Explanation:

Q: Does a Taylor series always converge to its generating function? Explain.

A: Click to see the answer

Q: What is a parametrization of a curve in the xy-plane? Does a function y = ƒ(x) always have a paramet...

A: Parametrization of a curve in the xy-plane:Parametrization of a curve consists of both equation and ...

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c. zx-pla...

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0 

Q: Substituting t=0 for the inital equation qoul get <-1,02>, and again with the derivative foem,...

A: Given

Q: How do you graph equations in polar coordinates? Include in your discussion symmetry, slope, behavio...

A: Description:The polar equations are sketched in the polar coordinates by analysing the symmetrical s...

Q: In Exercises 1–3, give a geometric description of the set of points in space whose coordinates satis...

A: Hi there! Thank you for the question, but as per our guidelines we can solve only one question at a ...

Q: In a psychology experiment, a person could memorize x words in  f(x) = 3x2 − x  seconds (for 0 ≤ x ≤...

A: a person could memorize x words in  f(x) seconds where

Q: Replace the Cartesian equations in Exercises 56–61 with equivalent polar equations. 56. x - y = 3 57...

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

Q: In Exercises 25–26, express each vector as a product of its length and direction. 25. 5k 26. 3/5i+4/...

A: We’ll answer the 25th question since we answer only one question at a time. Please submit a new ques...

Q: Find the centroid of the region in the first quadrant that is bounded below by the x-axis, above by ...

A: It is given that the centroid of the region in the first quadrant is bounded below by the x-axis, ab...

Q: Condense the following log expression. -2log3(xy)+4/5log3(z)^10+log3(x+1)

A: Condensing the logarithmic expression.

Q: What is an alternating series? What theorem is available for deter-mining the convergence of such a ...

A: The alternating series test.

Q: How can you sometimes use power series to estimate the values of nonelementary definite integrals? T...

A: Click to see the answer

Q: Graph the sets of points whose polar coordinates satisfy the equations and inequalities in. 1. 0<...

A: Problem1:The given inequality is the collection of all circles with radius 0 to 2, including both. T...

Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second ...

A: Given:

Q: Which polar coordinate pairs label the same point? a. (3, 0) b. (2, 7pai/3) c. (-3, 2pai) d. (-3, 0)...

A: a) (3,0)If we add pi with the angle then the radius will change its sign. So, (3,0) becomes (-3,0+pi...

Q: Find a formula for the distance from the point P(x, y, z) to the a. x-axis.    b. y-axis    c. z-axi...

A: The formula for distance between two points (x, y, z) and (a, b, c) is

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be 

Q: Under what conditions can you find the area of the surface gener-ated by revolving a curve x = ƒ(t),...

A: Click to see the answer

Q: Determine whether the following statements are true or false:  1. ln(x')=[ln x]'  2. any continuous ...

A: The given statement is,

Q: Can someone show me how to get to the answer in the problem?

A: Given integral

Q: Give some typical parametrizations for lines, circles, parabolas, ellipses, and hyperbolas. How migh...

A: First of all, consider the cartesian form of the equation for the line.Then, consider the parametriz...

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure...

A: Since you have submitted two questions, we\'ll answer the first question. For the second question pl...

Q: Find all points that simultaneously lie 3 units from each of the points (2, 0, 0), (0, 2, 0), and (0...

A: Let such a point is (x,y,z)

Q: Solve the following initial value problem for u as a function of t: du/dt+k/ m u = 0 (k and m positi...

A: Plug du/dt = u' to make it first-order linear equation.

Q: Show that the line b2xx1 - a2yy1 - a2b2 = 0 is tangent to the hyperbola b2x2 - a2y2 - a2b2 = 0 at th...

A: Find dy/dx.Then find dy/dx at the point (x1,y1) by plugging x=x1 and y=y1

Q: Write equations for the asymptotes for the graph of 2 + Sr - 3 f(x) =

A: Click to see the answer