What is the value of y' for y =x ? A-) In B-) C-) Not exist D-) E-)

Q: Find the distance between the points. (4, 1, 5), (8, 2, 6)

A: The distance between the points. (4, 1, 5), (8, 2, 6) is:

Q: Evaluate the limit, using L’Hôpital’s Rule if necessary

A:  

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: Given   

Q: Find the limit values if they exist, possibly justifying that they do not exist.If the limits are ∞ ...

A:

Q: The position of an object moving along a line is given by the function s(t) = – 6t +36t. Find the av...

A: Given that, s(t) = -6t2 + 36t The formula to find the average velocity of the object over the interv...

Q: Integration review Evaluate the following integrals.

A: To solve:

Q: Use the appropriate formula to express the product cos 9x cos 2x as a sum or difference.

A: We will use the formula  With A=9x and B=2x  

Q: Suppose that the inequalities

A:

Q: Evaluate algebraic expression for the given value or values of the variable(s). 8x - y, for x = 3 an...

A: Given that  x = 3 and y = 4.      

Q: Graph each side of the equation, sin x - sin x cos2 x = sin3 x in the same viewing rectangle. If the...

A:

Q: How do we solve this using Divergence Theorem when the shape is not closed at the bottom? Also how d...

A: Consider the given vector field, The surface S is a four-sides of the cube [0,1] x [0,1] x [0,1]. H...

Q: Determine whether the given f(x) = x4 - 2x2 + 1 function  is even, odd, or neither. State the functi...

A:

Q: 106. y' = y² – %, Yı = 0 %3D

A:

Q: Solve: -2x - 4 = x + 5.

A: We subtract x from both sides  

Q: A machinist is required to manufacture a circular metaldisk with area 100 cm2 .(a) What radius produ...

A: Let the radius = r cm  So the area is =πr2 cm2 .    

Q: (a) Set up an integral for the area of the surface obtained byrotating the curve about (i) thex x -a...

A: (a) Assume we have given a frustum to find the surface area;  

Q: Consider the graph of the cubicy = x(x - a)(x - b), where 0 < a < b. Verify that the graphboun...

A:

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = xn, x = 1...

A: Given ,  

Q: Suppose the interval [2, 6] is partitioned into n = 4 subintervalswith grid points x0 = 2, x1 = 3, x...

A:

Q: Find each limit, if it exists.

A: We need to find the limit if it exists.

Q: Convert the following expression to the indicated base. a1>log10 a using base 10, for a 7 0 and a...

A:

Q: b) Let f(x) = x*(x? - 1) be a given function then i) FIND the intervals on which function is increas...

A: We have given the function

Q: ■ Find the derivative of the function. Simplify wherepossible.  y =  sin -1 ( 2x+1)

A: We will apply chain rule  

Q: x? y? Level curves Consider the paraboloid f(x, y) = 16 - 16 and the point P on the given level curv...

A: The equation of paraboloid is We have given That implies,

Q: Is there any reason to believe that there is always a pair of antipodal (diametrically opposite) poi...

A:

Q: Integer coefficients Show that the first five nonzero coefficients of the Taylor series (binomial se...

A: .

Q: The number of apples produced by each tree in an apple orchard depends on how densely the trees are ...

A: We have to maximize A(n) = n(900 - 9n) We find dA/dn    

Q: Calculus Question

A: (a) Given:  

Q: find all possible functions with the givenderivative. y' = √θ

A: We first separate the variables  

Q: Curvature Find the unit tangent vector T and the curvature k for the following parameterized curve. ...

A:

Q: Express the distance between the numbers -6 and 8 using absolute value. Then find the distance by ev...

A: Distance between -6 and 8 is |8-(-6)|.  

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A:

Q: Calculus Question

A:

Q: Let A be a nonsingular k x k matrix with k> 1. Show that. det [adj(A)] = [det(A)]*-1

A:

Q: Find the area of the region bounded by the curves y = x²-2x and y= - x.

A:

Q: Sales A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x...

A: This is a quadratic function, and it must be maximum or minimum at the vertex. We can find x coordin...

Q: Find the derivative of the algebraic function.

A:

Q: Use the simpson's Rule to estimate the integral below. Be sure to show your function values, and a t...

A: To determine: The value of the given integral using Simpson’s rule with 4 subintervals.

Q: Computing the derivative of ƒ(x) = e−x

A: Given function is

Q: Use the formal definition of limit value (the "-δ definition") to show that:

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST QUEST...

Q: (1– 1)y' – y² +x²y+2x = 0, Y1 = -x² %3D

A:

Q: Find the minimum value of ∣sin x + cos x + tan x + cot x + sec x + csc x∣ for real numbers x.

A:

Q: Which of the series, and which diverge? Give reasons for your answers. (When you check an answer, re...

A:

Q: Determine whether the function y = 3 cos 2x is a solution of the differential equation y(4) − 16y = ...

A: y = 3 cos 2x We need to check whether the given function is the solution of the differential equatio...

Q: If you make a straight-line projection from Fig. 1.5,what will be the minimum feature size in integr...

A: Given function is At year 1970 Figure shows DRAM feature size versus year.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.