Determine whether the following statements are true or false. If true, provide justification. If false, provide a counterexample i.e. an example that shows that it is possible for the hypothesis of the statement to be satisfied, but not the conclusion. You may choose to give an algebraic expressions or graphs as counterexamples. (a) If f(1) = 2, then lim f(x) = 2. x→1 f(x) x>0 g(x) (c) If lim f(x) exists and lim f(x) exists, then lim f(x) exists. (b) If lim g(x) = 0, then lim does not exist. x→0 x→0- x→0+

Q: Let f (x) = x2 - 3 and g(x) = 2x + 1. Find (fg)(2). 2) ***HINT: Start by first finding f (2) and…

A: The given functions are,

Q: Show that f(2) =

A: We will show that derivative does not exist using definition. Then we will use geometry.  Calculate…

Q: Let f(x) f-¹(x) = 1 x + 11

A: we need to find the inverse of the function.

Q: 5. Find the V.A. and H.A. of the function 6-9x Sex a). f(x) : b). f (x) : 2x+5 2ex-1

A: Vertical asymptotes: The line x=L is a vertical asymptote of the functionf(x), if the limit of the…

Q: Find S f(x)dx if f(x) = [2 for x<2 [x for xz2

A:

Q: the graph of a function of the form f (x) = ax2 + bx + c, where a  0?

A: The function of the form f(x)=ax2+bx+c,a≠0  is a quadratic equation of first degree. The terms a, b…

Q: Find the value of x where the fuction is discontinuous.     f(x)= x2 + 3 if x>2       = 3x + 1 if…

A: We have given the function

Q: x+3 10. At which points do the functions y = fail to be continuous? If any, are x2-3x-10 the…

A:

Q: (x - 3, if xsC x+ 2, if x >c g(x) = Given the function find g(c + 1) so that g(c-1) 0. %3D

A:

Q: 4 Compute f(g(x)) where f(x) =x* -x and g(x) =x²-11. dx The answer is

A:

Q: Let f (x)=x* +2x – 3.x? – 4x +4. Find: (a) the intervals on which f (x) is increasing or decreasing.

A: Given that:  f(x) = x4 + 2x3 - 3x2 -4x + 4   find intervals on which f(x) is increasing or…

Q: Two identical circles of radius r are inscribed in a rectangle as shown. ∞o (a) Express the area of…

A:

Q: 3. Consider the relation f (x) = 2x² – 4. Find the f(x). Be sure to use proper notation.

A:

Q: (x2 – 4x lx + 2 if x > 2 2. Let f(x) = f(x) = find f (5). %3D %3D if x < 2

A: This question is related to functions, We will solve it using given information.

Q: 2x : 1 3 is not one to one True False

A: Given: The function f(x)=2x : 1≤x≤3x   :  x&gt;3

Q: Let f(x) ƒ-¹(x) = = 1 x + 13

A:

Q: 1.) Let f(x) = 7 + What is f(3 + h)?

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.