a. fx) = tan x b. g(x) = cSC x cos x c. h(x) = sin x d. k(x) = T

Q: Sx) - 2x? - 4х + 3

A: Given:- f(x) = 2x2-4x+3 To find:- Intervals on which each function is continuous.

Q: Is there a function that is both even and odd?

A: Yes, f(x)=0 is both even and odd.

Q: f(x) = 3x² - 2x-2, [-1,2]

A: To determine if the function   is continuous over the interval [−1,2], we need to check three…

Q: On what intervals are the following functions continuous?

A:

Q: y -2

A:

Q: 2x if x + 1 el/z I < -1. if -1 <I < 0 if if d) (*)f(x) = %3D I = 0 1/c

A: Checking continuity at x=-1 L.H.L limx→-1-fx=limh→0f-1-h                  =limh→02-1-h-1-h+1…

Q: Cx² f(x) = = if x 1 { 6 C-X

A:

Q: x rational 0, x irrational. x. g(x) =

A: We have to find

Q: Find all the numbers for which the function is discontinuous.

A: A function is discontinuous at a point if the functional value is not defined at that point. There…

Q: h(k) = V5 – k + Vk + 9

A: Note:- Square root function is not defined at negative numbers.  Square root function is continuous…

Q: 7. 4- 3- -7 -6 -5 -4 -3 2 6. -3- -4 -5- -6- -7 2)

A: Given that, The graph of any function is given. We have to find ithe interval in which the function…

Q: F:[- 2,2]– R, F(x) = L((- 3(² + 1) dt

A: We have F(x)=∫-2x2(t-3)(t2+1)dt       Apply Liebnitz's rule for differentiation under integration…

Q: On which intervals below is the given function increasing ?

A: First , I have written the definition of increasing function and then using the graph on different…

Q: Which . functions are continuous through its domain?

A: Continuous Function: A function fx is continuous at a point c of its domain if  limx→cfx=fc 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.