y= h(x) 1 -1 1 2 3 2.

Q: \S(cos x)dx = 0 %3D

A: Let us consider f is continuous even function. Let f=x2 So, fcosx=cosx2=cos2x…

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: f(x) = -7x + 6 x² +6 if x < 0 if x 20

A:

Q: x+5 4. f(x) = %3D x2-5x+4

A:

Q: The third interval of the following function xe* - 1, which between 0 and 1 is [2,3]. True False

A:

Q: Is f continuous at x = 4? (2.0) 1 2 3 4 5t -5 4 -3 -2 -10 Yes O No

A: We have to check whether the given function f(x) is continuous at x = 4 or not.

Q: 6x if x 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Identify the real number at which it is not continuous of the given function

A: To find: The real number at which the function is not continuous: Given: The function is fx=-x23x+9.…

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

A: We have to find

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

A:

Q: (x² + 1 if x -1

A: For function g(x) to be continuous on -1 limx→-1-g(x)=limx→-1+g(x)=g(-1)…

Q: f(x) x² - 2x - 8 { *2-22-3 x-4 x = 4 x‡4

A:

Q: h(k) = V5 – k + Vk + 9

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

Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

A:

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: The function f(x, y) -{¹. - x² - y², 0, if if x² + y² 1 , is continuous

A: Given function is fx,y=1−x2−y2, if x2+y2≤10,             if x2+y2&gt;1. We have to check whether the…

Q: -5-4-3 -L-1 I 234 5 6 where is the function discoutinuous

A: We have to find the interval

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…

Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

A:

Q: Graph the function Ax) = 4x-1, if x <-1 Determine if the function is continuous x-3, if x2-1…

A: The given function is  f(x) = 4x-1x-3if x&lt;-1ifx≥-1 A function is said to be continuous at a point…

Q: Determine the values of x where the function f (æ) is not continuous. Label each discontinuity as…

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.