2. Show by definition that the function f: [0, 0) → R where f(x) = V is continuous on R. Hint: you have to consider two differen cases: (i) continuity at > 0; (ii) continuity at = 0. Note in the second case, one can only approach = 0 from right, i.e. case (ii) is basically lim f(x) f(0). %3D T→0+

Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

A: 3)Given:

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: Let ce (a, b). If ƒ (x) is a function that is continuous at c, then lim,e- [f (x)] = lim,»c+ [f…

A:

Q: x? sin(1/r) if r + 0 if x = 0. if x + 0 f (x) = %3D

A:

Q: Answer the following True or False: If lim f(x) exists, then f(x) is a differentiable function at x…

A:

Q: 3. Describe the interval(s) on which the function is continuous. c) S(x)= x-1 2, x= 1

A:

Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

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

A:

Q: flx) = Jx-7 Lim f(3+h)-f(3) ||

A:

Q: Does limx → -1+ ƒ(x) = ƒ(-1)?

A: From the graph we see that at x=-1 there is a closed circle and the graph is right continuous at…

Q: 2. Evaluate lim,.

A: (1) Consider the provided limit, limx→91x-191x-9 Find the limit of the above expression. Simplify…

Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

Q: Give a pair of functions f: R →R and g : R →R such that g is not tangent to f at 0 and yet lim,0…

A: To give a pair of function f : ℝ→ℝ and g : ℝ→ℝ such that g is not tangent to f at 0 and yet limx→0…

Q: y=f() 3 6. Use the graph of f(x) above to find the value of the folllowing: lim f(x) =

A: At any point P limit exist if , left hand limit and right hand limit and value of function at P are…

Q: 7. Explain why for any function g, limg(c +h) = lim g(x). Use this to show that f'(c) = lim f(x) –…

A: Consider the given function limh→0gc+h=limx→cgx

Q: Use the limit definition to find the derivative of f(x) = 5x? + 2x – 7 at x = -2. Show all 1. :…

A: Consider the provided function, fx=5x2+2x-7, x=-2 find the derivative by using the limit definition.…

Q: Use limit definition to find f'(2) for the function, f(x) = 3x? – 4x + 1-

A: fx=3x2-4x+1 substitute x+h for x fx+h=3x+h2-4x+h+1 fx+h=3x2+2xh+h2-4x-4h+1 fx+h=3x2+6xh+3h2-4x-4h+1…

Q: 3. Show that the function | sin(2.x)| is not differentiable at r = 0 but the function | sin(2x)|1+T…

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.