Exercise 15. If f(x) = a cos(log x) + b sin(log x). Show that x² f(n+2) (x) + (2n +1)x f(n+¹) (x) + n(n+1)y(n) = 0

Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + 4i is %3D Log(-12). O 2i -12 None of them O…

A: We have to find Derivative using definition and L'Hospital Rule.

Q: The maximum value of F in F(x) = - 4 cos x is 2 4 1

A: We know range of cosine function is [-1,1] Therefore maximum value of f(x)= -4cosx is, f(x)=-4cosx…

Q: for: Q1) Find dx 1) y = log3(3x³ +x²)² x In(sec-1 /ã)

A: I have solved question 1 for next question repost.

Q: Let f(x) = cos(x2). Then f(20)(0) = %3D

A:

Q: Let h(x) f(æ) If f(x) = 3 cos (x) and g(x) = 3x + 2x2 – x + 4, what is h' (x)? (æ)6

A: Given: f(x)=3cos(x)g(x)=3x3+2x2-x+4   Let h(x)=f(x)g(x).   Then, h(x)=f(x)g(x)=3cos(x)3x3+2x2-x+4

Q: Determine the lowest positive real root of f(x) = 8 (Sin x) (e-*)–1 using the Secant method. Take…

A: Solution: Given that

Q: Describe with a sketch the end behavior of f(x) = cos x.

A: Given:            f(x) = cos x  The cosine function oscillates between values -1, 1 as x→∞ Hence it…

Q: Find f if f"(x) = 2+ cos(x), f(0) = 2, f(t/2) = -2.

A:

Q: #3. Prove that 2 = tax [- i log ( 1+12) K] tiz 2

A: Using the results:

Q: Find L {f(t)} if f(t) = cos 5t + sin 2t

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Q: If f(x) = cos(2x), then f"|

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: dy Q1) Find dx for : 1) y = log3(3x3 + x2)2 x In(sec- x)

A: I supposed to do only first question as our company guideline. Please repost other question as next…

Q: If f(x) = cos x, then f'() = A. B. - C. - C. D. √3

A:

Q: IfI(u) = [log, (1-2u cos x+ u' )dx, then prove that, I(u)+I(-u)-DI(u²).

A:

Q: Let f(x) = x³ + √√. Then f'(1) = 02 O 1.5 O 3.5 04

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Q: Find h" (x) if h(x) = log,(cos(x)) – e®z. -

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Q: Determine f,(x); f(x) = cos(2x³ +n²)

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Q: Find f if f"(x) = 2 + cos(x), f(0) = -10, f(x/2) = 4. %D %3D f(x) = iii

A: Recall: ∫xn dx= xn+1n+1+c; where c is an integration constant. ∫sinx dx= - cos(x)+c; where c is an…

Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: 1.Let  f(x)=cos(2x)+3x. Find (f-1)'(1).    2. Simplify the following expressions  a)log9(square…

A: Solve it.

Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A: