How do I solve the limit as x goes to -1 for the expression (sin(3x-3))/(1-x) without using l'hospital rule and solving it algebraically?

Q: Iff(x) = 3 x- 2 x, find f'(x)

A:

Q: f(x) = |x| · : %3D Then f-l(x) = if x > 0, and f-l (x) = if x < 0.

A:

Q: Find the derivative. [5x(x6+1)4]=? Answer is 5(x6+1)3(25x6+1). How did they get this answer?

A: Given

Q: If f(x) = 7 sin-(*), then f'(2) - =

A: dsin-1xdx = 11-x2 dxndx=n.xn-1

Q: 4) Find the derivative from FIRST PRINCIPLES of √(x) = 2√x (You will need to rationalize the…

A:

Q: If f(x) = (x + 1)( x + 2), find f'(0)

A:

Q: Show that for any real constants a and b, where b > 0, (n + a)» = ©(nº)

A: To show for any real constants a and b where b &gt; 0, n+ab=Θnb

Q: how

A: Que seems some data missing. Though I have simplified the given expression as much as possible.…

Q: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

Q: Find the derivate of this function]: a) f(x)= 9x²³+24x² - T F'(x) = b) f(x) = 4x³ + 9x²-9. F'(x) =…

A: (a)  f(x)=9x3+24x2-πd dx(xn)=nxn-1d dx(constant)=0

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: given  f'(x)=2x-1/2-3 find f(1)=0, and find f(x)  use basic calculus to find the answer thank you

A: given f'(x)=2x-1/2-3 , if  f(1)=0 then  find f(x)  use basic calculus to find the answer thank you

Q: 3 Find the interval on which f(x) =x'e x- is increasing.

A:

Q: O 16xsec²(4x²)tan(4x²)

A: Given that the function

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.