-2 Given f(x) = ²√4 - t² dt, evaluate the following. -2 (i) f (-1) (ii) f(0), by interpreting f (0) as an area

Q: . A family wants to build a fence in their backyard for their dogs, but the cost for the previous…

A:

Q: (sinhz)(coth’z+csch*r)dz

A: Integration is done.

Q: Find the capital value of a fort at a strategic location, where the annual rent is $750,000, paid in…

A:

Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0

A:

Q: an = an-1/n

A:

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

A:

Q: etermine the instantaneous rate of change of the function πt √√x sin (772³) dt : x = 1. x3 1 + √t

A:

Q: u=-5), v=-1-√31 (a) Find u-v. U-V= (b) Find the angle between u and v to the nearest deg 0

A:

Q: = ²/²/² ( e ² + e^²^²) 3. Obtain the Maclaurin series for cosh x using the fact that cosh x =

A: Given the function,   cosh x=12ex+e-x

Q: 5. sech 2x tanh 2x dx sech

A:

Q: I. Evaluate the following limits. sinh r2 → r2 1. lim z→0 sinhr 1

A: We will apply DL hospital rule more than once to solve this question.

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2, y = 1, and…

A:

Q: JO π 3 sec³ x tan x V √2 + secx dx

A:

Q: 5) Find the Maclaurin Series for f(x) = ²² +₂²²²₁ exte tex 2

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: y = coux, X = Find the are a OF i) sketch the area. ii) Determine the boundarier by ) Set-up the…

A:

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A:

Q: Solve the following matrix equation for a, b, c, and d. a-b b + c |-|8 8 3 88 3d+c 2a - 4d a = b =…

A: We will find the value of a ,b ,c ,d by solving the given matrix equation in the following step.

Q: Annual sales (in millions of units) of a certain model of phone are expected to grow in accordance…

A:

Q: Solve the differential equation of order one.  (x4 + 2y)dx - xdy=0 STEPS: a. Put the equation in…

A: Separate the equation to form standard form then solve

Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? O 0 02 Ο ΝΑ x-coordinate of the…

A: Solution is given below:

Q: -0.03t The function f(t) = 9000 e represents the rate of flow of money in dollars per year. Assume a…

A: The present value

Q: Find the area in square units bounded by the following: (Show graph and detailed solution. Box final…

A: Here, the area bounded by the curves: y=x3+1 and x-axis  with the limits x=0 and x=3 is:

Q: Draw a direction field for the differential equation y'= (y - 9)². Based on the direction field,…

A:

Q: Test for exactness then solve. (1 +  y2)dx + (x2y + y)dy = 0

A:

Q: -.f x³ ex² dx 3

A:

Q: find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to the plane…

A: We have to find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to…

Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? 00 O 1 02 04 ONA x-coordinate of the…

A:

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A:

Q: I. Directions: Determine if the function is continuous on the given interval 1-3. f(x) 2 12-x² ; [1,…

A: 1. fx=212-x2; 1,32. fx=2-x+3; -3,-13. fx=1if x≤2x2-3if x>2; 2,4

Q: Find the area of the region bounded by: 21. x + 1 = 0, x-3 = 0, y + 4 = 0 andy-5=0. 22. 2x + 3y = 6,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find y'. Show the step-by-step solution. Simplify your answer. 2x 1. y = In 4x²-1 2. y = log(tan x³)…

A:

Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

A:

Q: 2. Using power series, evaluate lim x → 0 sin x-x 3 X

A:

Q: -0.03t The function f(t) = 9000 e represents the rate of flow of money in dollars per year. Assume a…

A: Given that,

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the marginal profit.

Q: too (-1)³²x²² 4) Let sinx= -1=0 2ntl a) Find a power series for xsinx b) Differentiate the power…

A: Here is the solution:

Q: Q1-A/Find the domain of the following functions. 1-f(x) = √(sin(x) - 1) 2-f(x)=-/In(5x-x²/4)

A:

Q: A window has the shape of a square surmounted by a semicircle. The base of the window is measured as…

A: Given that a window has the shape of a square surmounted by a semicircle. The base of the window is…

Q: Find the area bounded by y = 2x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE

A:

Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

A:

Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

A:

Q: VI. Determine the instantaneous rate of change of the functio: sin (³) f(x) = V² siz r³ 1 + √t at x…

A:

Q: Find the Integrating Factor (I.F) of the following linear differential equation: (1 + ²) + y = t…

A:

Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: 6. Find the area bounded by y= In x, y = 0 and x = e.

A: Area of a curve y=f(x) bounded by x=a, x=b is given by, A=∫abf(x)dx ln(e)=1, ln(1)=0

Q: C. Find the slope and the equation of the tangent line to the curve. 23. y 2x−x+2 at (-1,5) 24.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: x-1 x² + 5x + 8 S dx

A:

Q: Find the volume of the parallelepiped determined by vectors , and

A: Find the volume of the parallelepiped determined by vectors &lt;3,1,4&gt;, &lt;2,0,2&gt; and…

Q: 1. -3 Given that 9+x² following functions: (−1)n+1 Σn=0 32n+1 1. f(x) = 5 arctan x2n. Obtain the…

A: We have to obtain power series representation.