Evaluate the convolution, f(t) * g(t) = 10t *t², then evaluate at t = 11.

Q: Find the convolution f (t ) *g(t) f(t)=t,g(t)=1

A: By definition of convolution we have

Q: Describe the long run behavior of f(r) 478 – 5r + 5r + 2 As r → 00, f(r) → ? As r → 0, f(r) ? v

A:

Q: 7. Find c such that f(c) = fave where fave is your answer to the previous problem.

A: (7) The function is given as , fx=x3 find c for fc=fave where fave is average value of f on 0,27.

Q: (a) Find the nested from of f (x) = tan³x – 3tan²x – 2tanx + 5 and hence find f(2.6) roundoff to 4…

A: We are given  f(x)=tan3x-3tan2x-2 tan x+5⇒f(x)=(tan2x-3tan x-2) tan x+5⇒f(x)=((tan x-3)tan x-2) tan…

Q: Find f(t). f(t) = = - 3s 1 - s²(s + 1)³

A:

Q: Suppose that G(t) gives the number of gallons of gas left in your car t hours after you started your…

A: (a). It is given that the function Gt represents the number of gallons of gas left in the car after…

Q: Calculate M6 for f(x) = v7x over [3,6]. (Use decimal notation. Give your answer to two decimal…

A: The function is fx=7x over 3, 6. The number of sub-intervals is n = 6. Obtain the step-size as…

Q: Q3: Find f'(5) for f(x) = x³e-x, h= 0.01 using three points formula, compute the error

A:

Q: c. Use antidifferentiation to find f (x).

A: Since, we have asked for solving part-(c) only.Since here it is given that f'(x)=x2 ln x -(i)Here…

Q: Let f(t) = (t-6)4 e3(t-6) u6(t). Find F(s)

A:

Q: 人 そはっけ)ことス,ソフ ク=ム Cうk CurlF 支ド = 22 ズ 0y a2 %3D -> (-出)5+ (号-)k !! よいF (ス)+ C)+塩(の)こ2 ニ Find a…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Given f(x) = In(- 4e" – 13), f'(x) = %3D

A:

Q: Q2g If DF(x) = f(x+h)-f(x) for fixed h then find sh (ex-)) = ?

A: We have to find the △h(e2x-1).

Q: Describe the long run behavior of f(t) = As too, f(t) → ? v As t→→∞o, f(t)→→ ? - 4tº + 2t6-3t5+1

A:

Q: Use the intermediate Value thereom to Show that gid=0 g(x)=0 on the interval E3,6] for quu)eメースメ-IS…

A: g(x)=x2-2x-15 on  [3,6]

Q: 3x2 Given that F(x) = In t dt, what is F'(x)? 3x 4 + t2 ||

A: Given, Fx = ∫3x3x2lnt4+t2dt  We have to find F'x.

Q: If f(x) = | V17+t³dt, then what is f(-1)?

A: Leibnitz Rule: Let f(x) be a differentiable function on closed interval a,b such that a,bare the…

Q: zt Find f'(t) if f(t)-ť° 8

A: The function is given by ft = t682t To evaluate : The expression of f'(t)

Q: Q8. Let f(x)= Ln(土) dt (6) Evaleata f'(10) = ? (b) Enlnts (Fツ (o)=? (f-)) (6) =?

A:

Q: If S f(t)dt : 3x2 + 12x, what are the possible values of a? Verify that your values of a are…

A: The given integral relation is: ∫axf(t)dt=3x2+12x From the fundamental theorem of calculus,…

Q: Find the convolution f (t ) *g(t) f(t)= g(t)=sint

A:

Q: find the critical point and classify it. a. f (x,y) =xlny + x2 -4x -5y + 8

A: The answer is given below:

Q: Let f(t) = t*e3. 4

A: Differentiate w.r.t to t

Q: F(X)=x" 2ny dorsn't this haveoninfiection. paint 20here f"(x)=0?

A: By taking derivatives, f(x) = x4   ----> f '(x) = 4x3

Q: Find De f Re ー X - 2 2SXミ-1 y = P(x) = ーX+2

A: The domain of a function f(x) is the set of all values of x at which the function is defined i. e…

Q: Q2: Let f(x) = 2x e-,x> 0 and Let Y = X2.Find G(y)and g(y). %3D

A: Implicit functions are the functions are not directly expressed, these are always expressed in terms…

Q: 2. Find the Maclaurik a. f(x) = 2. la f ....

A:

Q: Describe the end behavior of f(t) = 4tº – 4t8 – t6 + 5 - As t → - 0, f(t) → As t → 0, f(t) → ?

A: Given that - f(t)=4t9-4t8-t6+5 To Determine- End behavior of polynomial.

Q: Q2.Let The deswative f ù f CaJ= %3D

A: The objective is to find the derivative of the function.

Q: Find f(t). 2s s3 ]) «(-| f(t) =

A: Given that  Inverse Laplace of {e^(-2s)/s^3) To find Laplace transformation

Q: B1. Given the function T(n) = n3 + 20n + 5, show that T(n) is 0(n³)

A: Given The given expression is Tn=n2+20n+5.

Q: Describe the long run behavior of f(t) = - (t + 3)°(t + 1)(t + 2) As t → - 0, f(t) –→ ? As t → 0,…

A:

Q: Find f(t). 5s - 1 s²(s+ 1)- f(t) =

A: A detailed solution is given below.

Q: Describe the long run behavior of f(t) 3t° + 3t – 4t2 – 5 As t → – , f(t) → ? As t → o, f(t) → (?

A: Given the function f(t)=-3t8+3t5-4t2-5. We need to find the long run behavior of the function f(t)…

Q: Determine where A(t)=t^2e^5-t is increasing and decreasing.

A:

Q: Q11: Let f(x)=xr° + 3x³ d +x-10. Find dx (5"(48) .

A:

Q: Find the solution using homogenous function substitution of the following DE Show that 2xyy' == x² +…

A:

Q: Determine Rn(x) for f(x) = 1ln(x) about x = e

A:

Q: Find fogo h. f(x) = x* + 8, g(x) = x – 6, h(x) = Vx

A:

Q: What is the domain of f(x)=Dsin1(IIn(x)l)? %3D Select one: O (0,e] O (0,00)

A: Given, fx =sin-1lnx  We have to find the domain of  fx =sin-1lnx

Q: If you know f(t) = L-'{F(s)}, how would you fine L-{F(8)/s² j?

A:

Q: Approximate V126 using Ay f'(x) · Ax

A: Given,  126

Q: Q6) Compute the averoge value of the function, flx) = (7x²+ 3x + 5.3)e* on the interval [3,7]. %3D

A: Average Function Value: The average value of a function f(x) over the interval [a, b] s given by,…

Q: Find f'ox) for the Jollowing funchion. f(x)=x²ln 9X

A: As we know that; The Power law; ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Chain rule:…

Q: Describe the long run behavior of f(1) = x2 As a - ? v 00, f(z) → As a 0o, f(æ) v? -> Check Answer

A: Given function is: f(x)=x2 To evaluate the limit of function at x→-∞ and x→∞. Draw the graph of…

Q: O Caloulat 2nd hounene f(x)= sT こ>×ラ0 2. う2×23 With flx)> f(x+3n) Yne 忍

A:

Q: Use the grapn of g(x) below to answer what follows 4 3 2 - 2 -it'23 4 5 4 1-

A:

Q: Q2\Find T.E of the function f (x) = e2x when a =2?

A: Given that  f(x)=e^(2x) To find teh T.E

Q: t f ex) =J3x find the difference Quatient of f-

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.