COS X x2 + 3x +1 lim 200 7x2 4. lim x-0 3x + 1 2л + 4 x² + 1 ear lim 1 5. lim x--1+ x2 – 2x – 3 - x2

Q: y"+y' - 2y = x2

A: Solution :-

Q: using the definition of the derivative (i.e. limit process)

A: f(x) = x2 - 5x + 12

Q: The goal of this problem is to compute the value of the derivative at a point for several different…

A:

Q: 0.1sin(0.1) find the limit value

A: Given : e0.1*Sin(0.1)

Q: Using the limit definition of derivative, compute the derivative of the following function. No…

A: by limit definition of derivativesf'(x) =limn→0 f(x+h)-f(x)hf(x) = 3x2-2xf(x+h) = 3(x+h)2- 2(x+h)

Q: Using the definition of the derivative, prove that (d/dx)(e^x)= e^x. You will need to use the…

A: To show the derivative of ex is ex, by using the definition of derivative.

Q: sin x — х сOs X lim х — sin x

A: We have to calculate the value of limit.

Q: Jim sec x -COS X 2

A: Explanation and solution is given below....

Q: 3. Let f(x) and let a>0. Using the definition of the derivative 2+Va as a limit, find f'(a). Your…

A:

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary lim sin(5x)…

A: Given,          limx→0sin5xcsc9x

Q: Complete the sentence below. Iff is a one-to-one function and f(3) = 6, then f(6) = If f is a…

A: One one functions

Q: Can you be more specific with demonstration, prove its continuity in interval (2,10) and calculate…

A: A polynomial function is defined as a function consisting of one or more terms, each of which is the…

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.