1 台(1+ p)P> (1 + p)t•P > 0 k=1

Q: Write a formula for the general term (the nth term) of the sequence 2, 6, 10, 14, . . . ; a20. Then ...

A: Given: 2,6,10,14,............,a20 according to given data given sequence is arithmetic sequence whos...

Q: find the Taylor polynomials of orders 0, 1, 2, and 3generated by ƒ at a. ƒ(x) = sin x, a = π/4

A: Given:          f(x)=sin x, a=π4 Pn(x)=fa+f'a1!x-a+........+fkak!x-ak+fnan!x-an                     ...

Q: Find an equation of the tangent line to the parabola y=x2  at the point P(1,1)

A: To find an equation of the tangent line to the parabola y=x2 at the point P1,1

Q: Differentiate the function.

A: Given: y=2xlog10x To Find: Differentiate the given function. Concept: i. Product Rulef·g'=f'·g+f·g'i...

Q: Computing gradients Compute the gradient of the following functions and evaluate it at the given poi...

A: fx, y=sin3x+2y Partially differentiating with respect to x, we get fxx, y=cos3x+2y·∂3x+2y∂x=cos3x+2y...

Q: Find general solutions of the differential equation  9x^2y^2+x^(3/2)y'=y^2

A: Given differential equation: 9x2y2+x32y'=y2

Q: Surface area and volume Let f1x2 = }x and let R be the region bounded by the graph of ƒ and the x-ax...

A: Given that, fx=x33

Q: Evaluate the integrals ∫2eθ cosh θ dθ

A: To evaluate  ∫2eθ coshθ dθ

Q: Dividing the cheese Suppose a wedge of cheese fills the region inthe first octant bounded by the pla...

A: From exercise we have  ∫04 ∫04 ∫0y dzdydx =∫04 ∫04 z0ydydx=∫04 ∫04 ydydx=∫04 y2204 dx=∫04 162dx=∫04 ...

Q: The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a heig...

A: Given V=khbwherek=a constanth=heightb=the area of the base

Q: Use properties of logarithms to expand the logarithmic expression log(x/1000)  as much as possible. ...

A: Given logx100

Q: Simplify : (27)-1/3

A: The expression given is (27)-1/3 Simplify the expression , The cube root of 3 is 27. 27-13=33×-13=3-...

Q: Calculate the derivative of the following functions

A:

Q: Find the length and width of a rectangle whose perimeter is 21 meters and whose area is 20 square me...

A:  

Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3) x<...

Q: Differentiate  cosx/x

A: The given function is f(x) =(cosx)/x       = x-1.cosx

Q: Evaluate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or in...

A: Here given limit as   limx→111-x-21-x2orlimx→111-x-21-x1+x

Q: Write inequalities to describe the sets The slab bounded by the planes z = 0 and z = 1 (planes inclu...

A: The slab has a three dimensional coordinate system which includes the length,  breadth and width of ...

Q: Describe in words the variation shown by the given equation : z = k√x/y2

A: Given: z=kxy2 To Describe: Describe in words the variation shown in the given above equation.

Q: Use the most appropriate method to solve the equation cos2 x + 2 cos x - 2 = 0 on the interval [0, 2...

A: Given: The trigonometric equation as cos2x+2cosx-2=0 for x∈[0,2π), To find: The solution of given eq...

Q: Integrals in cylindrical coordinates Evaluate the followingintegral in cylindrical coordinates.

A: We know that,  x = rcos(θ)  ,  y = rsin(θ)  and  z = z in cylindrical coordinate system. Here we hav...

Q: Determine whether the following series converge. Justify your answers.

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y = 2x² + 1 ...

A:

Q: Find the center C and the radius a for the spheres (x - 1)2 + (y - 2)2 + (z + 1)2 = 103 + 2x + 4y - ...

A: Standard equation of sphere is given as x-x12+y-y12+z-z12=r2, where x1,y1,z1 is center of sphere and...

Q: A solid lies between planes perpendicular to the y-axis at y = 0 and y = 4. The cross sections perpe...

A: Given, y=0 and y=4  parabola x=10y2

Q: Find parametric equations for the given curve. Line through (1, -2) with slope 3

A: we know that equation of line which passes through pointx1,y1 and slope is m given by y-y1=mx-x1    ...

Q: Use properties of logarithms to expand the logarithmic expression logb(x2y) as much as possible. Whe...

A: logbx2y

Q: What are inflection points? How do you find them?

A: Inflection points are the points where given function changes their concavity means from concave dow...

Q: describe the given region in polar coordinates. The region enclosed by the circle x2 + y2 = 2x

A:

Q: Find the area of the region bounded by the graphs of y = 2e−x , y = 0, x = 0, and x = 2.

A: Given equations: y=2e-xy=0x=0x=2 The region bounded by the graphs of these equations is shown below:...

Q: g(x) = [x +3 if x ≥ -3 and -(x + 3) if x < -3] Evaluate : a) g(0) b) g(-6) c) g(-3)

A: g(x) = [x +3 if x ≥ -3 and -(x + 3) if x < -3] Evaluate : a) g(0) b) g(-6) c) g(-3)

Q: Find the axis of symmetry for the parabola whose equation is given . Use the axis of symmetry to fin...

A: fx=3x+22-5 Comparing with fx=ax-h2+k, we get a=3, h=-2 & k=-5 Therefore axis of symmetry is, x=h...

Q: The volume of a pack of orange juice is 800 mL correct to the nearest 10 mL. (9a) The actual volume ...

A: Given: Volume of one pack of orange juice=800 milliliter, correct to the nearest 10 milliliter. For ...

Q: Find the inverse Laplace transform of: (b) - .2

A:

Q: 33-36 - Linear Functions Given Graphically The graph of a linear function f is given. (a) Find the r...

A: The graph of the function f is: The graph of f is a straight line passing through the points (0, 3)...

Q: Decide whether the integral is improper. Explain your reasoning.

A: Given- ∫12dxx3 To decide- Whether the given integeral is improper. Concept Used-  Using the power ru...