Deduce then that (explain show all the details) F (а - а) + F(а+ a), F (cos (ax) f (x)) (a) F (a – a) – F (a +a) F (sin (ax) f (x)) (@) 2i

Q: If F(x)=sin(7-x5-13-x³ +5-x). Calculate dF(x) = dx

A:

Q: 4) | tan (x). sec(x) dx

A:

Q: Suppose that f(2) = 2. f'(2) = 8, g(2) = 2, and g'(2) = -2. If F(x) = (f • g)(x) and G(x) = (g •…

A:

Q: Determine f'(x) for: Ax) = sin (5x - 2)

A:

Q: f(x)=sinx is a function(explain) a) one to one b) on to c) not

A: A function f : A→B is one to one if each element of Set A has a unique element on Set B. In…

Q: 3. Solve the following equations over the interval [0, 2π]. Use exact values where possible, or…

A: a) tan2x=13 tan2x=13tan x=±13x=π6,7π6,5π6,11π6

Q: g(x) f(x) = Sinx)" g()=1 g)=0. Find Let and Select one: -2 None -3/2 E/3

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Q: ことる ーx (x+2)(X-2) -6x (x -ax+4) y" CX+2) (x-1)3 need first derivative Eanalysis %3D (x-2)3 (x+2)°

A:

Q: f'(1). et f(x) = 3x 6x-7 Find f'(x).

A: Given query is to find derivative.

Q: d? -(sin-'(x²)) dx2 2– 4x4 A 3 2– 2x4 B 3 2+2x4 3. 2+4x4 D

A: Here we have to use the concept of derivative

Q: If f(x) = sin x, show that f(x + h) – f(x) = sin x cos h – 1 sin h + cos X h h

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Q: бх + 3 f(x) = In 5х — 3

A: Given: fx=ln 6x+35x-3 To Find:  f'x=?

Q: d dx f(x)=sina, f(0) = 7.

A:

Q: 9. 10. If f(x)=√ex, the derivative is: √ex a) f'(x) = Vex b) f'(x) = √ex c) f'(x) = 2x Which of the…

A: Calculate the derivative of both problem in the following way:

Q: 5) Differentiate f(x) = √3x² + 4x.

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Show that the function f(x)=x^-4 +cos(-2x) is even, odd, or neither."

A: Given, f(x)= x^-4 +cos(-2x) f(x)= (1/x)4 + cos(-2x)

Q: Evaluate (*(x-2) (х-1)3

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Q: f'(3i) = -i, g(7+ 2i) = 3i, g'(7 +2i) = -4. Find (f o g)'(7+2i). 4i -4i 2.

A:

Q: d dx x= ||

A: Given that

Q: F) y= 4x³ In(8x)

A: y=4x3ln8xd dx(xn)=nxn-1d dx(lnx)=1xd dx(ab)=b×dadx-a×db dxb2

Q: cosx sec? x + cos x csc csc? x csc? x secx cos? x cos x cos x E f(x)dx _ 2 1. If f(x) 1 , then

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Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: /is [sec2(x) – csc²(x)]dx Evaluate:

A:

Q: (d) v1+ tan x =1+;x

A: To prove that the following approximation holds, 1+tanx≅1+12x

Q: the derivative. 28) y = x5/6 A) 5x7/6 B)x1/5 a C)/x-5/6 D) Ex-1/6

A: Since you have asked multiple questions in a single request we would be answering only the first…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.