5. у %3D sin?(3x? — 1) 6. Р() %3D 4csc(sin3t) ans. y' = 6xsin(6x² – 2) ans. P'(t) = -12(cos3t)csc(sin3t)cot (sin3t) |

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution. 

Q: The slope of curve is given as (2x + b+) and has a value of 17 at x = 2. What is the value 16 of y w...

A: Topic = Integration

Q: b. Let g(x) = x² – 7. Determine the root(s) of g. 7,-7 Preview 7 = 7., – 7 = -7. c. Let h(x) 5x? - 3...

A: Topic = Algebra

Q: Question 4 of 10 2 -10-8 -6 -4 -2 2. 4. 6. 10 -6 -10 y 10 4 -10 -8 -6 -4 -2 2 4 6 8 10 -6 -8 10 y 1...

A:

Q: Q4 (a) By using properties of Laplace Transform, find (i) The Laplace Transform of f(t) = 2e sin 4t,...

A: Let's find. 

Q: Equation Find Given dy dx 3. y = (a) when x = 4 %3D dt dt dx dy (b) when x = 25 = 2 dt %3D dt

A: Solution: y=x 

Q: J, 4. lim X-3 x2 - 9 x - 3 lim X3 x2 – 2x – 3 5. X - 3 lim X"i x2 – 2x – 3 6.

A: We need to find limit.

Q: What is an antiderivative of ... x²+1 x + arctan x – 5 2x + 3 x + arccot x x + 2arctan x + 1 А) в B)...

A:

Q: Find f'(t) for the function f(t) = est +sin(t) 2t Do not simplify the expression you get. 2t(3et +co...

A: To find f't of the given function.ft=e3t+sint2t

Q: Test the series below for convergence using the ratio test. n+ 2 24n +1 n=1 The limit of the ratio t...

A: Given: ∑n=1∞ n+224n+1where f(n)= n+224n+1Ratio test : l=limn→∞ an+1anif l<1 then the series is co...

Q: Question 11 Зсos3x-1 To evaluate f scos - dx, the integrand can be transformed to 1-sin?x A.) [(3cos...

A: We put 1-sin2x=cos2x and then solve it. Follow 2nd step.

Q: Explain what it means to say that: lim, h(x) - o and lim h(x) x →5+ – 0.7. x →4 As x approaches 5 th...

A: According to question,Given limits,limx→4 hx = -∞,andlimx→5+ hx = -0.7,

Q: Find the center of mass of a thin plate of covering the region between the x-axis and the curve y = ...

A:

Q: If f. g and h are functions defined on the set of real numbers defined by: F(x)= 3x+1, g(x) = 2x -1 ...

A:

Q: Show that f(x,y) = 1-x* - y* has a relative maximum, even though D in the theorem is 0. The critical...

A: Given : f(x, y) = 1 - x⁴ - y⁴

Q: B In Problems 17-34, use implicit differentiation to find y' an evaluate y' at the indicated point. ...

A: Given:-ey=x2+y2 ; (1, 0)differentiate both sideseydy=2xdx+2ydyeydy-2ydy=2xdxey-2ydy=2xdxdydx=2xey-2y

Q: (a)Odd degree polynomial functions have opposite________ .  (b) When we multiply two functions toge...

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as...

Q: VI– 2e* dx

A: Given that a integration and we solve the solution of this integration by using general property of ...

Q: Bin decides to fly to Hono, Maui from Seattle, a distance of 2,678 miles. His plane travels at 567 m...

A:

Q: cos(2x)81-x (x*+1) Given f (x) = Use logarithmic differentiation to find the derivative of the funct...

A: According to question,Given function,fx = cos2x81-x4x2 + 1

Q: 4. A certain computer algorithm used to solve very complicated differential equations uses an iterat...

A:

Q: At what x values in the interval [0, 27] does the function f(x) = sin² (x) – sin(x) have a %3| horiz...

A: Given that: f(x)=sin2x-sinx

Q: (αv) ^(rv (φλq) ^ Γv )]

A: The given statement      r∨p∧~r∨p∧q∧r∨q

Q: Express the given quantity as a single logarithm. In(a + b) + In(a - b) – 8 In(c)

A:

Q: 20. Find the equation of the curve for which y" = x, and which through the point (1, 2) and the tang...

A:

Q: 2. (D2 + 3D)y = -18x: v = 0. Dy = 5 when x = 0

A: Given differential equation is  D2+3Dy=-18x  and the given conditions are y=0, Dy=5 when x=0 find th...

Q: What value(s) of o are an appropriate choice when proving the following limit? lim (2 + 9x + 25) = 5...

A:

Q: Sm(e*)dx = 6? ¿9 =: What is the value of a so that A.) 0 В.) 1 C.) 2 D.) 3

A: We have to find the value of a

Q: What should be the rewrite of the integrand ofSAS dx so that the resulting integral is integrable? (...

A:

Q: For f (x) = Vx – 3 +1 Find the derivative function of f' Evaluate the derivative at x = 4 Find the e...

A:

Q: x* + x³ + x² – x + 1 – x + 1 x(x² + 1)²

A:

Q: The half-life of cesium-137 is approximately 30 years. If an artifact initially contains 100 g of ce...

A:  decay constant k=ln2half life

Q: Question 1: When working with rational functions of the form f (x) = P(z) what information can you 2...

A: We can find domain of f(x)   

Q: Solving by variation of parameters 4y" 4y'- 8y 8e-*, we find that: O u_1=(-2/9) e^(-3x)and u_2=-(2/3...

A: Auxiliary equation and variations parameters

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9. 32 A.) s.u. B.) 18 s.u. C.) 36 s.u. ...

A: Follow the procedure given below.

Q: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How fas...

A:

Q: The definite integral (-+ dx when evaluated is equal to- 11 Find the value of a." 12 ... -8 1. 3.

A:

Q: dx 3.

A:

Q: 5dx If Verz+1= 2, what is the value of b? %3D A.) 2 B.) 4 C.) 8 D.) 9 A D B A

A:

Q: Linear differential equation hith constart coefficients. 3 D = n- 4R+ 6) y

A: Given: D4-4D3+7D2-4D+6y=0

Q: 2.

A:

Q: (x + Vz)°da

A:

Q: 1. Find the indicated values. f(g(8)) |x| f(x) g(x) s(8(5)) 1 5 g(f(5)) 2 5 8(5(3)) 3 2 4 4 1 S(S(4)...

A: Use the given table for finding the value of function 

Q: An object is shot upwards from ground level with an initial velocity of 3 meters per second; it is s...

A: Let's find. 

Q: f(x,y) = 100x062y0 38. Find the marginal productivity of labor and capital.

A:

Q: Evaluate the difference quotient for the given function. Simplify your answer. f(a + h) – f(a) f(x) ...

A: We have to use the given formula to calculate the difference quotient

Q: Determine if the given functions f(x) are continuous or not at the given value of x. Show your compl...

A:

Q: 4. Find the value of k so that the value of f,"(2y – 1) dy is 10. а. 1 b. 2 с. 3 d. 4

A:

Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3 c...

A:

Q: Given f (x) = {r²+ k_ if-1< x skx – 3 if x<-1 | . Find the value of k such that lim f(x) exists. X--...

A: Topic = Functions