# Let f(t) be a function defined for all values of t. The Laplace Transform of f(t) is defined by: F(s)= �ç[∘,�‡](e^-st(f(t))dt). If the improper integral exists, Find the Laplace Transform for F(t)=t^2

26,363 results
1. ## Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of a and b #2. Let h be a

2. ## Calculus

A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and the graph of f has a point

3. ## Calc

Given function f defined by f(x) = ( 1- x)³. What are all values of c, in the closed interval [0,3], that satisfy the conditions of the Mean Value Theorem?

4. ## Math

The function f is defined by f(x)=2x^2-6x+5 Find the set of values of p for which the equation f(x)=p has no real roots. Thanks in advance!

5. ## Math

The functions of f(x), g(x), and h(x) are defined below: f(x) = -2x g(x) = 2x + 5 h(x) = x^2 + 3x - 10 Calculate the indicated function values. 1. f(a+b) 2. f(g(x))

6. ## AP CALC. AB

Let h be a function defined for all x≠0 such that h(4)=-3 and the derivative h is given by h'(x)=(x^2-2)/(x) for all x≠0 a). Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local maximum, a local

7. ## calculus

Q.NO.3: Show that the function z=tan^-1(2xy/x^2-y^2)satisfies Laplace’s equation; then make the substitution x=r cosθ, y= r sinθ and show that the resulting function of satisfies the polar form of laplace’s equation

8. ## Calculus

Let f be the function defined by f(x)= x^3 + ax^2 +bx + c and having the following properties. 1. the graph of f has a point of inflection at (0,-2). 2. The average value of f(x) on the closed interval (0,-2) is -3. Determine the values of a,b and c

what is the Laplace transform of e^4t(cos 2t) ?

10. ## Math

Evaluate the piecewise defined function at the indicated values. f(x) = x^2 if x < 0 x + 9 if x ≥ 0 f(−3) = f(−2) = f(0) = f(2) = f(3) =

11. ## calculus

Let f be the function defined by f(x)= sqrt(x), 0

12. ## multivariate calculus

Q.NO.1: Show that the function z=ln(x^2 + y^2)+2tan^-1(y/x) satisfies Laplace’s equation. (∂^2z/∂x^2)+(∂^2z/∂y^2)=0

13. ## Calculus

Find the Laplace transform of: f(t)=t-2e^(3t)

14. ## Calculus

Hi! My question is: Given that f is a function defined by f(x) = (2x - 2) / (x^2 +x - 2) a) For what values of x is f(x) discontinuous? b) At each point of discontinuity found in part a, determine whether f(x) has a limit and, if so give the value of the

15. ## Algebra

The function g is defined below. g(x)=((x)^(2)-9x+14)/((x)^2-11x+24) Find all values of x that are NOT in the domain of g. If there is more than one value, separate them with commas.

A quadratic function is defined by f(x)= 3x^2+4x-2. A linear function is defined by g(x)= mx-5. what values(s) of the slope of the line would make it a tangent to the parabola.

17. ## Algebra

Complete the table for each function. 1. f(x) = √x The x values are 0, 1,4 and 9. The corresponding y values that I got are 0, 1, 2 and 3. 2. g(x) = -1/4√ x The x values are 0, 1, 4, and 9. The corresponding y values that I got are 0, -1/4, -1/2 and

18. ## Calculus-HELP!!!

Find the Laplace transform of: f(t) = cos^(2)(2t)

A quadratic function is defined by f(x)= 3x^2+4x-2. A linear function is defined by g(x)= mx-5. what values(s) of the slope of the line would make it a tangent to the parabola

20. ## Algebra

The function h is is defined below. h(x)=48x^2+ 12x - 16 Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas. I'm lost.

21. ## Math-Algebra II to be exact

Come up with a new linear function that has a slope that falls in the range −1< m

22. ## Calc

The function f is defined by f(x)= (25-x^2)^(1/2) for -5 less than or = x less than or = 5 A) find f'(x) B) write an equation for the tangent to the graph of f at x=3 C) let g be the function defined by g(x)= (f(x) for -5

23. ## Math

A quadratic function is defined by f(x)=-3.7x^2+6.8x+4.2. A linear function is defined by g(x)=-0.5x+k. Determine the value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth

24. ## Math(algebra)

1.) Consider the function F defined by the equation: f(x)=3x+2 a.)find each of the values F(1),F(2)and F(3). I need help on figuring out the steps on this killer

25. ## Need help asap

I need help! Reasoning: Can a function have an infinite number of values in its domain and only a finite number of values in its range? If so, describe a real-world situation that could be modeled by such a function. Writing: What is the difference between

26. ## Calculus-PLZ HELP STEVE!

Find the inverse Laplace transform of the following function: F(s)=(9+s)/(4-s^2)

27. ## math 234 calc 4 !!!!!!!!!!!

write this function in terms of heaviside functions, and then show your work in finding its laplace transform f(t)= o if o < t

28. ## Calculus-HELP!!!

Find the Laplace transform of: f(t) = cos^(2)(2t)

29. ## differential Equations

laplace transform of f(t) = t sin (at) use integration by parts

30. ## Differential Equations

Use the Laplace Transform to solve this initial value problem. y'''' - 8y = 0, y'(0)=63, y''(0)=216, y'''(0)=297 I would really appreciate the help.

31. ## math 116

What is the difference between domain and range? The domain of a function is the set of all values for the independent variable (in the following example, that's the x) for which the function is defined. That is, if you have a function such as f(x) = 1/x

32. ## Algebra

Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater

33. ## Calculous

let f be the function defined by |x-1|+2 for Xor equal to 1. where a and b are constants a)if a=2 and b=3 is f continious for all x? justify your answer b)describe all the values of a and b for which f is a continious function c) For what values of a and b

A function f is defined by f:x→x+10 over x-8,x not equal to 8.Find the values of x for which f^-1(x)=x.

35. ## Math

Evaluate the piecewise defined function at the indicated values. f(x) = x2 + 6x if x ≤ −1 x if −1 < x ≤ 1 −1 if x > 1 f(−2) = f(-3/2) = f(−1) = f(0) = f(35) =

36. ## D.E

A particle moves on the x-axis with an acceleration, 246msta. Find the position and velocity of the particle at 3t, if the particle is at origin and has a velocity of 10ms when 0t by using either the method of undetermined

37. ## Calculus

Consider the function of defined by f(x)=x^3/3-4/x a. Find the X values for the points of inflection. b. Determine the intervals where the function of f is concave up and concave down.

38. ## math

1.Transform the graph of f(x) = 3^x to sketch g(x) = 3^-(x+1) -2. Show table of values and each transformation clearly. 2.Write two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y = 3. Investigate whether

1.Transform the graph of f(x) = 3^x to sketch g(x) = 3^-(x+1) -2. Show table of values and each transformation clearly to get full marks. 2.Write two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y = 3.

40. ## Math

Determine the representation in the frequency domain function f (t) below, through the table of Laplace transforms: f (t) = 6e ^ -(0,2+3t ) f (t) = e^-t sen(3t)

41. ## calculus

i'm having trouble with a problem in my calc class...it isn't really calculus yet since we're still in the review section but it goes somethign like this: ( don't have it in front of me) a rational function is defined by: R/(x-K) where R and K are

42. ## Clueless in calculus

The function f is defined by f(x)= (25-x^2)^(1/2) for -5 less than or = x less than or = 5 A) find f'(x) B) write an equation for the tangent to the graph of f at x=3 C) let g be the function defined by g(x)= (f(x) for -5

For any real number x there is a unique integer n such that n≤x

44. ## calc 2

(last one) ... Let f(t) be a function defined for all values of t. The Laplace Transform of f(t) is defined by: F(s)= ç[∘,‡](e^-st(f(t))dt). If the improper integral exists, Find the Laplace Transform for f(t)= sinhat

45. ## Calc2

Let f(t) be a function defined for all values of t. The Laplace Transform of f(t) is defined by: F(s)= ç[∘,‡](e^-st(f(t))dt). If the improper integral exists, Find the Laplace Transform for F(t)=t^2.

46. ## calculus

Find the inverse Laplace transform of the function: F(s)=1/(s(s+1)(s+2))

47. ## Math

Using the table Laplace transform, determine the function f (t) of the following functions F (s). F(s)= 1/s^2 + 3s/s^2+9 F(s)= 6/s^2 + 10s+29 F(s)= 1/2s + 8/s^2+4s+8 - 3/s^2

48. ## Calculus--Steve plz?

Find the inverse Laplace transform of the function: F(s)=1/(s(s+1)(s+2)) ...A special thank you to Steve who has already been a tremendous help! Thank you so much =)

49. ## Differential equations

My homework question is to find the Laplace transform of the function f(t)=e^(10-2t)*step(t-5). I am not sure how to handle the e^(10-2t) portion of the equation. Thanks in advance.

50. ## domain

Find the domains of f and f' 1, f(x) = xe^x 2. f(x) = x^(3/5) 3. f(x) = x/(x-2) TIA 1) R 2) It's the interfal from zero to infinity for f but for f' it is this inteval with zero excluded, because unlike f, f' is singular at zero. 3) Here only the point 2

51. ## ODE

what is the laplace transform of 5/2.e^t-3/2.e^-t

52. ## Calc 3

What is the laplace transform of: f(t) = 0, 0

53. ## college math

the Laplace transform of e^4t(cos 2t)?? please i need help. thanks

54. ## Math

What is the laplace transform of (t^2)sin(t)?

55. ## math

solve y"+4y-4z'=3x z"+z-y'=1-x where y(0)=z(0)=1 and y'(0)=z'(0)=0 by laplace transform

56. ## Math

inverse laplace transform of {5/(s-4)^3}

57. ## calculus

Solve the DE by using the Laplace transform: x''+x=cos(3t), x(0)=x'(0)=0

58. ## differential equation

Find the Laplace transform by using the theorem of L{f(t-a)H(t-a)}=(e^-as)F(s) L{(e^4t)H(t-10)}

59. ## ODE

what is the laplace transform of cost+4sint

60. ## Calculus

Find the inverse Laplace transform of: F(s)=3/(s-4)

61. ## Calculus-HELP!!!

Find the inverse Laplace transform of: F(s)=2/s^4

62. ## differential Equations

laplace transform of f(t) = t^2 sin (at) use integration by parts

63. ## ODE

compute the inverse laplace transform 2S^2+13S+5/(s+3)(s-1)^2 i got 3e^t+5e^t+3e^t, not sure it correct

64. ## domain

How do you find the domain of log(x^2-4)? and how about this one? e^(3x+4)? Please help me! Well kristie, you might recognize log(x^2-4) = log((x-2)(x+2)) and then use a property of logs to see it as a sum, i.e., log(ab)=log(a)+log(b). You are then

65. ## Calculus

A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and the graph of f has a point

66. ## Intermediate Algebra

Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater

67. ## Intermediate algebra

Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater

68. ## math

Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater

69. ## algebra, logarithms

Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater

70. ## algebra

Describe the values for x that may not be appropriate values even when they are defined by your classmates’ function

71. ## AP Calculous

let f be the function defined by |x-1|+2 for Xor equal to 1. where a and b are constants a)if a=2 and b=3 is f continious for all x? justify your answer b)describe all the values of a and b for which f is a continious function c) For what values of a and b

Function f and g are defined by f:x→4-x and g:x→px^2+q where p and q are constants.Given that the composite function gf:x→x^2-8x+11,find the values of p and q.

73. ## Calculus HELP!!!

Here is the graph. h t t p : / /goo.gl/PTc2I (spaces added at the beginning so it could be added as a website) 1. Let g be the function given by g(x)=integrate from -4 to x f(t)dt. For each of g(-1), g'(-1), and g''(-1), find the value of state that it

74. ## pre-calculus

for the function f defined by: (x)=3x^2+3x+2;find the following values. a. f(-1)= b. f(-x)= c. -f(x)= d. f(x+h)=

75. ## For the function defined by...HELP

For the function defined by f(x)=3x^2+5x+2, find the following values. (a) f(-4)= (b) f(-x)= (c) -f(x)= (d) f(x+h)=

76. ## math

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function

77. ## Precalculus

The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function

78. ## Calculus

Suppose f(x) is a differentiable function with f(-1)=2 and f(2)=-1. The differentiable function g(x) is defined by the formula g(x)=f(f(x))' A. Compute g(-1) and g(2). Explain why g(x)=0 must have at least one solution A between -1 and 2. B. Compute g'(-1)

79. ## Calculus

For which values of r does the function defined by y=e^(rt) satisfy the differential equation y''+ y'-6y = 0

80. ## math

Consider the function defined as f(x)=(x^2+2x+3)^2+4. As x ranges over all real values, what is the minimum value of f(x)?

81. ## MAth

Describe the values for x that may not be appropriate values even when they are defined of your classmates’ function.A function could, for example, indicate the amount of bone strength (y) in a living human body over time in years (x). It would not make

82. ## math

The function y = 3x - 6 is defined for all values of y less than 12. Determine the value of x that corresponds to the upp boundary y = 12. a)54 b)2 c)18 d)6

83. ## MAT116- Algebra 1A

What is the difference between domain and range? Describe a real-life situation that could be modeled by a function. •Provide feedback about your classmates’ answers. Describe the values for x that may not be appropriate values even when they are

84. ## algebra word problem

Describe the values for x that may not be appropriate value even when they are defined by a function A function could, for example, indicate the amount of bone strength (y) in a living human body over time in years(x) . It would not make sense to look at

85. ## Algebra 2B

Come up with a new linear function that has a slope that falls in the range −< < 1 0 m . Choose two different initial values. For this new linear function, what happens to the function’s values after many iterations? Are the function’s values getting

86. ## Algebra

Today I did a practice SAT problem. If the function ƒ is defined by ƒ(x) = 2x + 3, and if ƒ(a) = 11, what is the value of a? A. 4 B. 7 C. 11 D. 17 E. 25 This is the correct answer and the explanation Here's Why: If the function ƒ is defined by ƒ(x) =

87. ## Function plz help!!!

If a function u(x,y)=arctan(y/x) deduce the laplace equation of the function. plz show working i don't no where to start from...plz thanks

88. ## calculus

For x including [–15, 13] the function f is defined by f(x)=x^7(x+4)^6? For x including [–15, 13] the function f is defined by f(x)=x^7(x+4)^6 On which two intervals is the function increasing (enter intervals in ascending order)? ( i was able to get

89. ## calculus

Q.NO.1: Show that the function z=ln(x^2 + y^2)+2tan^-1(y/x) satisfies Laplace’s equation. (∂^2z/∂x^2)+(∂^2z/∂y^2)=0

90. ## math

1.Transform the graph of f(x) = 3^x to sketch g(x) = 3^-(x+1) -2. Show table of values and each transformation clearly. 2.Write two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y = 3. Investigate whether

91. ## Math

i am trying to transform a piece wise function, but my problem is that the lines are so irregular i cant tell if it is correct. i can't even tell the equation of the lines I'm attempting to transform. y= -2/3 x -6 if -9

92. ## math

Let f be the function defined on {-3, 1} by f (x)= (x+1)/x^2+ax+b and (C) its representative curve in an orthonormal system . Knowing that the two lines of equations x=1 and x=-3 are asymptotes to (C) calculate the values of a and b.

93. ## Calculus

I posted this several days ago but it hasn't been answered and I still can't figure it out: For which values of r does the function defined by y=e^(rt) satisfy the differential equation y''+ y'-6y = 0

94. ## cal3

Using the chain rule, find the min and max points and their values of the composite function defined by: z= x^2 + y^2, x=sin(2t), y=cos(t)

95. ## Algebra

Totally lost here! Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of

96. ## differential

solve dT/t=k(T-Tm(t)) using laplace transformation, where Tm=50+20U(t-h) and where U = unit step function.

97. ## Maths

Correct each of the following incorrect statements: 1)The inverse of the function defined by y= 5/x +1 is defined by y= 5/x - 1. 2)The graph of a function and its inverse are always reflection in the line =0.

98. ## calculus

Consider the function f(x)=x^n for positive integer values of n. (a) For what values of n does the function have a relative minimum at the origin? (b) For what values of n does the function have a point of inflection at the origin?

99. ## Algebra

Can anyone help me with the following, by providing the steps to get there and what it is that you are doing? any help would be greatly appreciated... We define the following functions: f(x)=2x+5 g(x)=x^2-3 h(x)=7-x/3 ◦Compute (f – h)(4). ◦Evaluate

100. ## Calculus

A function f(x) is defined by: f(x) = { m * sinx + n, if x 2 pi. a. Given that f(x) is a differentiable function, find the values of m and n. b.Write the equation of the tangent line to f(x) at x = 2pi. c. Use the tangent line equation to find an