Find the derivatives of the following functions. Simplify as much as possible by com- bining like terms and canceling common factors. (a) y= 2sec(5z) %3D

Q: = 2x2 + 2y? and Find the center of mass of the solid S bounded by the paraboloid z = the plane z = 6...

A: Let x=rcosthetha and y=rsinthetha  So, x2 + y2 =r2  So, r very from 0 to √3 

Q: Convert the point from rectangular coordinates to spherical coordinates. (-8, –8, V7)

A: The given point -8,-8,7

Q: 2. Given: f(х) - х* +4x? - 2х+9 g(x)=x² +2 h(n+2) = 2h(n+ 1)– 3[h(n)] h(1) =1 and h(3)= 5 f(-5) с. h...

A: Given, fx=x3+4x2-2x+9 hn+2=2hn+1-3hn2 ; h1=1and h3=5 We have to find f-5 and h6.  

Q: Choose the most appropriate answer: Evaluate the integral : S dx 7x6 x7+1 O In(x7+1) + C O In(x"+ 1)...

A: Let's find. 

Q: 192 Chapter 3 Differentiatio 27. Sports A baseball diamond has the shape of a square with sides 90 f...

A: Given query is to find the rate of change of distance.

Q: (7) (y sec 2x + sec x tan x)dx + (tan x + 2y)dy = 0 (8) () ds + () dt = 0 (9) (2x³ – 3x²y + y³) = 2x...

A:

Q: Find the surface area of the solid that results when the region in the first quadrant bounded by the...

A:

Q: 2. x10 – 3x6dx tane d0 In (cose) 3.

A: Here we have to solve the given indefinite integral.

Q: Using Laplace transform, find the solution of the initial value problem. 5. y" – 4y = 6e³t – 3e-t, y...

A:

Q: Need help with multiple choice!!

A:

Q: Convert the numeral to a numeral in base 16 621 10 4627 10-16

A: We divide 4627 by 16 until the quotient is equal to 0.

Q: uppose that yi (x) =x² denotes a nontrivial solution of a homogeneous linear econd-order differentia...

A: Put y1 =x2 then solve for y2 

Q: 15. A parabola has the following properties: axis vertical, passes through (-1,0), (5,0) and (1,8). ...

A: Topic = Parabola

Q: 18) Let n be the region in the xy-plane bounded by the curves Y=8xx² and y=x². Set up, but do not ev...

A:

Q: 6* – 2 - lim x→0 ekx +7 k = (If any value of k will work, enter any; if none will work, enter none.)...

A:

Q: determine the value of k which will make h' (π/4)=6 when h(x)=In(cosx)+kx. a. 6 b. 5 c. 0 d. 7

A: Given, hx=lncosx+kx We have to find the value of k for which h'π4=6  

Q: Describe the end behavior (long run behavior) of f(x) = x° As x → 00, f(x) → ? - As x → 00, f(x) → ?

A: The given function f(x)=x6

Q: Find the first and second derivatives of the function. Check to see that your answers are reasonable...

A: Solution is written in below steps.

Q: S (72³ + 4a²) dæ

A: Evaluate the integral ∫7x3+4x2dx  

Q: Find (fo g)(x) and (g o f)(x) and the domain of each. f(x) = x - 3, g(x)= 4x – 5 (fo g)(x) = (Simpli...

A: f(x) = x2 - 3 g(x) = 4x - 5 (f o g)(x) = f(g(x)), g(x) function is in f(x) function  f(g(x)) = [g(x)...

Q: dy (13) 2+ 3y = 3x²e¬3* dx

A:

Q: If R is the total resistance of three resistors, connected in parallel, with resistances R1, R2, R3,...

A:

Q: A model of a building is in the shape of a cube with a square pyramid on top. Each edge of the cube ...

A: Volume of the model is equal to sum of the volume of Cube and volume of pyramid

Q: d the equatiom of the tangent line to the curve xy – 7 = Vx + y² at the point (5,2).

A: For finding tangent line to the curve , find the derivative of the function and put the value of poi...

Q: Evaluate: J6e2 -x(x²)dx

A: Find your answer below 

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. E(- 1)n n ...

A: Given series is ∑n=1∞−1nn2⋅n+2!n!43n. Use ratio test Here, an=−1nn2⋅n+2!n!43n. Now,  limn→∞an+1an=li...

Q: Find (fo g)(x) and (g o f)(x) and the domain of each. f(x) = x2 - 3, g(x) = 4x- 5 (fo g)(x) =(Simpli...

A:

Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values ...

A: Given fx=x25-9x if -1≤x≤0if      0<x≤1

Q: What type of the conic section is this given equation: 4x2 5x +23 = 2 (10 – 2y²) %3D | O HYPERBOLA O...

A: please check the given equation. for given equation, none type of conic section exist.

Q: Given a function value of an acute angle, find the other five trigonometric function values. csc e =...

A: topic - trigonometric functions

Q: 1. Evaluate the following limits. x² + 3x+ 2 lim, →-1 x' +4x +3 2 а. х? — 2х lim,→2 b. Vx? +5 – 3

A:

Q: f(x) = 1 and lim g(x) 15. If lim = 2, then evaluate each limit. x→0 x→0 X f(x) b. lim x→0 g(x) a. li...

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Q: The concentration of a drug in the body decreases exponentially after a dosage is given. In one clin...

A: Here, the exponential equation is given by: P=P0ekt...(1) where P is the amount in mg after t hours ...

Q: 8 en Vn! n=0

A: We will check the convergence of the series. 

Q: Find the limit or indicate that it does not exist. lim t→L 5 i+ 4 sin i+ t k cos tan Select the corr...

A: limt→πsint2i+cos54tj+tan53tk

Q: Inverse Function: One-to-one   Running burns about 13 calories per minute. a) Determine the type ...

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Q: In 2012, 34.1% of all glass containers were recycled. A beverage company used 400,000 lb of glass co...

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Q: Evaluate dV, where E lies between the spheres x2 + y? + z2 = 4 and x? + y? + z² E x² + y? + z? = 36 ...

A: x​=ρcosθsinϕ y=ρsinθsinϕ z=ρcosϕ ρ2 = x2+y2+z2 ​

Q: Find the point of intersection of the lines given below and then find the plane determined by these ...

A:

Q: 6 Find the Maclaurin series for f(x) = %3D 1+x

A:

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series c...

A:

Q: Let f(x) be a function and let a be a real number. Determine if the statement is always “True”; othe...

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Q: Learning Task 2 Use reference angle and appropriate sign to find the exact value of each expression ...

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Q: dx the integrand is In x2 (A) True B) False

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Q: Using differentiation formulas, write the derivative with respect to x of the following. Find the su...

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Q: Given a differential equation rx" +21?x" - tx +x= 1212. Show that +c2t+c3t Int + 41² is a solution o...

A: We need to prove the differential equation.

Q: Let a be a real valued constant. If In(ax – 1) = 9 ,then x eº+1 | O True O False

A: Solution: lnαx-1=9, then x=e9+1α

Q: (4) Y dy ху+у? dx x2

A:

Q: More example implicit differentiation on For f(x, y) = 4x² + 9y² – 36 = 0, find y' when x = V5.

A:

Q: sin2x C. Evaluate lim- using table of values. Let x takes on the values 1.5, 0.8, X-0 0.5, 0.2, 0.03...

A: Given:limx→0sin2xx