Write an equation for the ellipse Q

Q: 4. If = tanx, show that the relation y' = 1 + tan²x.

A: Let's solve.

Q: Show that the vector field given below is conservative and find its potential function. F(x, y) =…

A:

Q: A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from…

A:

Q: Jonathan enjoys gardening. The east side of his house is 45 units in length. He can put 30 flowers…

A:

Q: 3f'(t) + 2f (t) = t where f(0) = -2

A: Let's solve linear differential equation.

Q: Example: find the complex Fourier expansion of the periodic function shown below f(x): = COSX TT --…

A:

Q: Find the area of the shaded region. 44) 2) (II/4, 2) TE: II II 2 311 4 y = 2 y = csc²x X

A:

Q: Evaluate [F·dr if F(x, y)=(x²y)ī +(xy²)ƒ and the curve C is given by r(t) = (t²)i + (t)j, 0≤t≤1.

A:

Q: . For what value(s) of x is the tangent to y = 5 (3x-12)4 horizontal? A) -103, 680 B) -4 C) 4 D)…

A:

Q: +31 Find the particular solution of the differential equation dy/dx = (4x^2-7x)/(3y^2+2) at x = 1,…

A:

Q: Find the average value of f(x, y) = x² y over the rectangle R with vertices (−3, 0), (−3, 8), (2,…

A:

Q: 12. If a graph is concave up on an interval, what happens to the slope of the tangent as you move…

A:

Q: If the equation y = 50x + 25 represents the amount of (y) money it costs to rent a car for (x) days,…

A:

Q: 6.What do you call the properties of vector when their cross product or dot product is equal to…

A:

Q: Graph the equation r2=81 sin (20). Use a graphing utility to check your work and produce a final…

A: Solution: Using the formula r2 = a2 sin(2θ), where a≠0 graph the lemniscater2=81sin(2θ)

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

A: Solution: F=<8xy,x2 -4y2 >; R : y= x(3-x) and y=0

Q: Consider the function f(x) = 12x³ + 45x¹ - 360x³ + 5. f(x) has inflection points at (reading from…

A:

Q: (2x + 3)y' = y + √2x + 3, when x = -1, y = 0

A:

Q: e Green's Theorem to evaluate [(-y²)dx + (x²)dy if the curve C is a triangle with rtices at (0,0),…

A: Top:- application of integration

Q: 2. Find the point where the tangent line to the curve f(x) = x²lnxis horizontal

A:

Q: [x = t - 1 Q.1 Verify that the lines L₁ y=1-t lz=1-t and find the distance between them. and [x = 2t…

A:

Q: Let f(x) = (x−³+4)5 – 1.

A: Assume that y=f(x) and use the description of f(x) and then express x in terms of y, that formula in…

Q: Find the Indefinite Integral. (Remember to use absolute values where appropriate. Use C for the…

A:

Q: The formula for the volume of a cone is given below. Find the rate of change of the volume for each…

A: We can answer the question as below.

Q: Consider the following. Function y = 7e1 - x2 (a) Find an equation of the tangent line to the graph…

A: Solution

Q: Evaluate the triple integral: π/2 2 S*S*¹² S² π/2 O 0 12p sin cos 0 dp do do

A: Given that a triple integration and we solve this integration by using general property of…

Q: How do you find a bata ratio? What is the formula?

A:

Q: 13) Eloise contracts to work for 11 ​days, receiving $0.04 the first​ day, $0.12 the second​ day,…

A:

Q: Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates, A = with…

A: This is  a problem related to integration of polar coordinates.

Q: Calculate Sc(x + y) ds, where C is the rectangle formed by de x=0, x=4, y= -1 and y=1

A:

Q: es and state values of 0 that produce the entire graph s the entire graph of the parabola?

A: We have to convert in polar form from the given Cartesian curve (parabola)

Q: Find the market equilibrium point for the following equations: Supply: .10x + 5 Demand: -.15x + 10

A:

Q: below is conservative and find its poter 3x²e³y +15y²z+2x²yz²)j + (5y³ + 2x²

A:

Q: 323. [T] The number of cell phones produced when x dollars is spent on labor and y dollars is spent…

A: The number of cell phones produced when x dollars is spent on labor and y dollars is spent on…

Q: Find a formula for the sum of n terms. Use the formula to find the limit as n Σ(++4)(#) Ilm Submit…

A:

Q: Use the Ratio Test or the Root Test to determine whether the following series converges absolutely…

A:

Q: A company that produces cell phones has a cost function of C = 20x² - 541x + 22940, where C' is the…

A: This question can be solved using the concept of maxima and minima.

Q: Find the limit. (Hint: Let x = 1/t and find the limit as t-ot.) lim 7x tan(2) Step 1 You are asked…

A:

Q: Write an equation for the parabola shown to the right. The equation of the parabola is (Use integers…

A:

Q: ← Find an equation for the hyperbola described. Graph the equation. Center at (-7,-6): focus at…

A:

Q: Find an equation for the hyperbola described. Graph the equation Center at (-1,-4); focus at…

A:

Q: Consider the following. f(x) = tan(x), (3,-1) (a) Find an equation of the tangent line to the graph…

A:

Q: Find the length of the curve. ¹) x = ¹ y 3/2 - y 1/2 from x = 1/2 from 4) 3 5) x x= 16 to x = 25 =…

A: If a function y=f(x) is defined on interval [a,b] the length of the curve is given as - Length (L)=…

Q: y = 14. If u +4 u-4 and U= √x + x 10 dy , find dx when x=4.

A: This question can be solved using the concept of derivatives.

Q: √3+2 px/3 ² √²³ (2² 10 (2 cos 0 - 3 sin 30) de dr

A:

Q: Two sides and an angle are given below. Determine whether the given information results in one…

A: Two sides and an angle are given below. To determine whether the given information results in one…

Q: Problem 4. A point P is often identified in mathematics using the notation P(x, y) to reference a…

A:

Q: A population of 450 bacteria is introduced into a culture and grows in number according to the…

A: Given, p(t)=4505+4t73+t2

Q: etermine the appropriate rotation formulas to use so that the new equation does not contain any…

A:

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: f(x) = x3 -3x2 + 3 here we have to find the relative maximum and minimum point  from second…