Q 2. (a). Show that limit x→1, does not exist if (3-2х f (x) = for x<1] 6х —4 for x21] (b). Show whether f (x) is continuous at x=-2, if (3х-2 for x=-2 f (x)={ x-2 for x+-2 x² – 4 1 Q 3. (a). Solve with the help of substitution method 2x *xp= (b). Show the traces and intercepts of x + y° + z² +3z+2=0 Q 4. Find the derivative of the following function by using ab-initio method. f (x)= 4x° +5x² -3x+1 Vcos x Jeos x+ V/sin x Q 5. Show that =dx= 4

Q: Suppose that 2 <f '(x) < 4 for all values of x. What are the minimum and maximum possible values of…

A: Using Mean Value Theorm.

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: (-3 if z 2

A: Here is a step by step solution of the problem. We have proved discontinuity at x=2 by evaluation…

Q: x*+6x3-1 4. Let p(x) = x5 + 3x² – 1 and r(x) = - x²+x-2 a. How many zeros could p(x) have and why?…

A: We have to solve first 3 parts according to the guidelines.

Q: 1. State the domain and range of f(x) = /9(x - 4) + 2 D:[2,00) A. D:[4,00) В. D:[4,00) D:[2,00) D.…

A:

Q: 7. Differentiate f(x) = (3x + x)² in three ways. When you have completed all three parts, show that…

A: Given that, fx=3x+x2

Q: Consider the functions f(x)= [x²-9 x*-1 2x ; x=-1 and (3x+2 g(x) = { x=-1 Define the new function…

A:

Q: 119. If f(x) = a*, show that f(A + B) = f(A) • f(B).

A: Given: fx=ax For finding fA+B, we put x=A+B in given expression and simplify it

Q: 5. a) Find the equation of any tangent(s) to the graph of f (x) = -x² + 6x + 5 that also go through…

A: Given

Q: The function f(x) - 4x³ +7.56x² + 366.2004x + 7.99 is increasing on the open interval ( = It is…

A:

Q: 5. Determine algebraically whether the function f(x) = -3x5(4-9x2) ¹2 is even, odd or neither.

A: "According to the guidelines issued by the company We are supposed to answer only one question.…

Q: 5. If f(x) = 2 x + 3 a) f-¹(g(x)) and g(x) = 21, find b) the domain and range of f-¹(g(x))

A:

Q: 15. Let f(x): = 4 e 1 and g(x)= 3x x + 5 Find the domain of (fg)(x).

A:

Q: 4. Let f-(x) = g(x) = x-5, k-1(10) + 7 = 10 and h(x) = then find: b. Domain of h(x). c. (hof)(2). (Z…

A:

Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

A:

Q: 5. Determine f,(x); f(x) = x*², x > 0

A: We need to find out first partial derivative

Q: 7. Consider the functions f(x) = 2x² - 7x + 4 and g(x) = -7x + 5. a) Find f(-1). b) When does g(x) =…

A: Function is f(x)= 2x2-7x + 4 .............(i) We've to find the Value of f(-1) Put the Value of x=…

Q: Write the domain in interval notation. 3) y (t)=√√√8-t 4) f(x) = x - 4 x-5

A:

Q: 2. State the domain and range of f(x) ==Vx +2 5 D:[-2,0) D:[-2.) В. D:(-0,00) C. D:[0,0) D. R:(-0,0)…

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.