Find a differential operator that annihilates the given function x²e ¬*sin (2x). A ((D+1)²+ 2) 2 B ((D+1)2+4) 3 ((D+1)²+2) 3 D ((D-1)²+2) 2 E ((D – 1) 2+4) 2

Q: find L1L2 and L2L1 for the given differential operators, and determine whether L1L2 = L2L1. 4. If L1…

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Q: Find the differential quotient of the following functions: a) f(x)=5x–2 b) f(x)=x2 +3 c)…

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Q: A 3. Find (f g)(x) if f(x) = x2+x +1 and g(x) = x2 - x- 1. %3D %3D O (f 9)(x) = a4+ 2a + 3x? +2x +1…

A: We can find (f·g)(x) as below

Q: Find a linear differential operator that annihilates the given function 1+6x-4x3

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Q: Y4(t) = ¿et is a particular solution of y" – y = 2e3t. The general solution of /" – y = 2e3t is…

A: We find whether the given statements are true or false.

Q: 1 | t(t + 3) dt -1

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Q: Find a formula for f (z) if f(z) = I+1 f '(z) =O ( )'(2) =D-

A: We will use concept of inverse function and differentiation of a function.

Q: Suppose R(x) = f(x)/3 − 5x2. Find R′(−1).

A: Derivative: - The function's spinoff is that the equation we have a tendency to discover. The…

Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: Let F(s) = 1 (2s − 1) (2s − 3) - Find f(t) = L-¹[F(s)]

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Q: Write the smallest differential operator that annihilates the given 3x +x²e + sin(5x) e3 sin…

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Q: Function f that is defined and differentable on all of R.  a. suppose h(x) = (x3 − 4x-1 + 5) ·…

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Q: If f(x)=3x-²-5x¯³+1 and g(x)=√√x, then derivative of (gof)(x) is: a. b. C. 1/1/23 1 2 3x ² 5x 3 1 d.…

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Q: Find the set of all values of a for which f(x) = x° +(a + 2)x² + 3ax + 5 is invertible.

A: We know that, for function to be invertible the discriminant of its first order derivative should be…

Q: (c) cos(t+ T/4)8(t) (d) (t+1)8(t)dt + 1)8(t)dt (e) (t – 5)dt +1

A: (c) Concept Used:-δ(t)={0if t≠0∞t=0Consider cost+π4δ(t)=cost+π4.0t≠0∞t=0Hence cost+π4δ(t)=0t≠0∞t=0

Q: Solve for F(s) L[(1+ e2t)²] a. 1 2 1 s's-2's- 4 Ob. 1 2 s - 2 s's+2 1 + s's+2' s + 2 d. 1 + s's-2' s…

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Q: Given g(x) = In(7x+x), the derivative g (x) is

A: Given,           gx=ln7x2+x

Q: Suppose f(t)=-H(t)-1²H(t)-3(t-1)H(t-1)+(-3) H(1-3)+(-5)H(1-5) Express f(t) analytically.

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Q: Show directly that the given functions are linearly dependent on the real line. That is, find a…

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Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: 2х + A A. If dx = In [g(x)| + C then x2 + 4x + 5 A = and g(x) = 2х + B В. If dx = In |g(x)| – tan¬…

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Q: 1. f(x) = x² 9 2. f(0) = cos(30) g(x) = 4|x|² 3. f(t) = et cos(ut) 4. f(x) = e³x 9 9 9 g(0) = 12…

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Q: The complementary function(C.F.) of the differential equation (D – 7)²(D + 5)y = 7x is O (c1 +…

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Q: 4) Consider the function F(x) = f f (t) dt . Find F¹ (7). O F(7)-F(2) O f(x) O f(7) Of(7)-f(2)

A: Given query is to find indicated derivative.