-4 -3 ✓ -2 T -1 √ -7 -6- -5 4 -3- 2 -1- 0 -1- -2- -3- -4- 8 X S 2 3 4 5 6 X 7 A function f(x) is continuous at an x value of aif and only if the following three conditions are satisfied: (1) f(a) is a defined real number (2) limf(x) is a defined real number (3) f(a) = limx→af (x) TRUE or FALSE: Only (3) fails. True Explain your thinking. √ False Share With Class

Q: Test the continuity of the following lons at tne points each (x+1, 3x- 1, 1 < x < 2; (i) x= 1, (ii)…

A:

Q: 15. Discuss the continuity of the function f (x) = x²-4. x-2

A: To find the continuity of function we need to find the domain of function

Q: evaluate the function. [3x – 1, if x 1 [3x – 1, if x 1 f(0) f(1) f(5) f(-4) g(0) 8(-3) g(1) g(3)…

A:

Q: Find constants a, b such that function f(x) given below is continuous on the entire Real line.…

A:

Q: Now it's your turn! Assume you have a new function: 9(x) = (2x+3)2(x-2)5 x³ (x-5)² ? Question The…

A: Part (a) Recall that a function is said to be increasing if the first derivative of the function is…

Q: Show that the function f(x)=x4 + 6x +1 has exactly one zero in the interval 1-1 01 Which theorem can…

A:

Q: Find the particular solution of the first-order linear differential equation for x > 0 that…

A:

Q: -a -1 for f (x) = { x + 2 x 3 Find f(-2)

A:

Q: O 4. For the function f(x) = x² – 3, Find f - 1/3-x² Ox-3 x² X 012-3 O 1-3 X (1)

A:

Q: Determine the domain and/or the range of the following function. 2х-1 [1] f (x) = (Domain only)…

A:

Q: (4ах + 2b , X<1 2х — 3Ь,1 <х < 3 (2ах + 4b g(x) ,3 <x Find the values of "a" & “b" if gm is…

A: We will find the value of a and b as following-

Q: (5) State the value(s) of x where the functions are discontinuous (x = a) AND the type qf…

A: Given that, fx=1               if x&lt;2x+3         if 2≤x≤47              if x&gt;4

Q: (2x² + 5, if x 5 Consider the function h(x) = Find the value of B such that h(x) is continuous at x…

A:

Q: Given the function f(x) (x+ 4)(x-7) 1o nonin alamos Give the value (or values) for which f(x)IS Not…

A:

Q: xydx – (x² + 3y²)dy = 0 -

A: