Jhe first appearance f l'Haspital rule was in 1696, in the first ever calculus textbook writein by Marquis de ľ' Hospital . The example used was to find imit f function y = 2ax-x* a faax as x→Q uhere a>o a Jaxs at this fime, con veuti an Was to write a as aa). Find the limit.

Q: - x + 1 If f(x) = find (fof) (x). X - 1

A: The composite function f∘fx is consist of two functions. Both functions are fx. We can also write…

Q: Find the limits in Exercis

A: Find the limit: limθ→0sinθsin2θ Solution: We know that, sin2θ=2sinθ cosθ Evaluating the limit.…

Q: Find the limits in Exercise

A: Limits are used to calculate the approaching value of the function at which the exact value of the…

Q: Problem 3. Use the Squeeze Theorem to find lim, ,0+ (2/4 sin E). Problem 4. Sketch the gronh

A: As per bartleby guidelines we only give first  questions answers.

Q: If f is a function and not necessarily a position function, then we can interpret AVa,a+h] as the…

A: This is a problem related to average and instantaneous rate of change of the function. Based on the…

Q: 4x-1 dx using right endpoints x = a+kAx.

A:

Q: State the definition of the derivative of a function f. Use the definition of the derivative to…

A:

Q: Consider the piecewise function if x 2 x² - 4

A: The function is said to be continuous at x=a If, limx→a-f(x)=limx→a+f(x)=f(a) The given function is…

Q: Express the limit as a derivative.

A: Our Aim is to evaluate the limit of the expression given below:-limt→πsin (t) cos (t)t-π-(i)

Q: Find the limits in Exercis

A: We can find the limit of an expression by applying the limit point to the variable in the expression…

Q: Find the limits in Exercise

A: Given, limθ→0cosπθsinθ we know expansion of sinx sinx=x-x33!+x55!-.... now put this expansion in…

Q: Find the limit (Please leave the answers in exact form) Use L'Hospital Rule, but please make sure to…

A: Given y=ex-e-xex+e-x

Q: Below is the graph of f(x), f' (x), and f"(x). State which graph belongs to which function and a…

A: The f'(x) tells about the slope of the function of f(x). So if f(x) is decreasing then f'(x) < 0…

Q: 3. Use the limit definition to calculate the slope of the tangent to the curve f(x) = x² + 3x-5 at…

A: The given curve is

Q: 1. Write the conditions a function has to meet in order to be continuous at point a. a) b)

A: A function f(x) has to meet these conditions in order to be continuous at any point a

Q: (a) Explain both mathematically and graphically what makes a function odd or even. b) Use the limit…

A: (a) Suppose fx is a function then mathematically it is said to be odd if  f-x=-fx And graphically, a…

Q: real mummber tzo ) if fex)= 20Vř, Show that for any f (t x) = VE +(a) 2) Consider the function fx)=…

A:

Q: lim x→0 4-Vx+16

A:

Q: a) f(x) at x = 0 b) fx) 3x at x = -4 X-7

A: a) f(x)=6x at x=0b) f(x)=3xx-7 at x=-4

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.