Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: Differentiate y = (-6+sinx)/(x+cosx)

A:

Q: Determine 3 sec(9x) tan (9x) dx

A: We have to determine the value of integral: ∫3 sec 9x tan 9x dx Solving given indefinite integral by…

Q: 8 him XT 2 (secx tanx) 1

A:

Q: Determine whether f(x)=sinx+cosx is an odd or even number

A: Given function is f(x)=sinx+ cosx

Q: Find f), (b) f(r) tan(2r)

A: To find f’(x).

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

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: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

A:

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: Calculate Sin(5x)=-√(2)/2

A:

Q: d dx x= ||

A: Given that

Q: tan(h2x) 2tan(hx) 1+ tan(h²x,

A: It is known that tanh2x=sinh2xcosh2x also sinh2x=2sinhxcoshx and cosh2x=cos2hx+sin2hx Substitute the…

Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

A:

Q: Evaluate tan° (x) sec* (x)dx in the two different ways indicated.

A:

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.