x² – 1 if x + -1 f(x) = x + 1 if x = -1 a = -1

Q: Sketch the graph of f.

A: Definition used-                 Graph of a piecewise function -                  We have to…

Q: Graph the following functions.

A:

Q: 4. f(x) = x(x- 2)(x + 1)(x + 3) 5. f(x) (x + 2)(x - 1)(x-3)2

A: According to company rule we can answer only first question and rest can be reposted.

Q: 1 3. f(x) = x - 2 at x = 2 %3|

A: In this question we have to determine the function is continuous.

Q: Find a formula for f-1(x) if 2 + 3 f (x): %3D 2 - 9 f-1(x) =

A:

Q: 1 f(x) %D x + 5 1 f-1(x) = X – 5 -

A:

Q: 1-х 26. f(x) =- х+2 27. /(х)- Vx* - 3

A:

Q: -4x+6 for x<-1 f(x) = x² +2 for 1<x<4 for x24 Part 1 of 5 f (3) =| Part 2 of 5 f(-2) = Part 3 of 5…

A: see below the calculation

Q: x2 - 8 If f(x) = X-4 where is f not differentiable?

A: Find where is f not differentiable

Q: - 2< x< -1 f(x) = {-2 -1< x< 1 .0 1< x< 2

A:

Q: 1. Let f(x) = {x²-3 if x<0 {x-7 if x 2 0 a. Find f(4) b. Find f(-3)

A:

Q: F(X)= x^3-18x^2+81X  inflection points occur at x=

A:

Q: 1. Let f(x) = { x² -3 if x<0 {x-7 if x20 a. Find f(4) b. Find f(-3)

A: This is Piecewise defined function so put the value of x according to defined in their respective…

Q: 1-6 for part A F(x)= 4•2^-x +1

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1 f (x) = - 1

A: Here we find domain of given function

Q: x²+2x=1 then f'(1) is Let f(x) = 2x3+1

A: we have given f(x). And we have to find f'(1)

Q: a. f(x) = e-6x about x = -4 b. f(x) = ln(3+ 4x) about x = 0 c. f(x) = – about x = -3 d. f(x) = 7x² –…

A:

Q: 6. Suppose f(x)-<ɛ. Solve for|x-1 where f defined below. x 1 f(x) = 2 3

A:

Q: Find S'(-1) if #(f(x))'+ 9z°f(x) = 2 and f(-1) = 2 I'(-1) =

A: To find f'(-1) first we differentiate both sides of  the given equation with respect to x and then…

Q: Graph the function

A:

Q: 3x -2 if - 4sx1 x² + 2x -1 if x< 2 Given f(x) = - and g(x) ={ x+3 5х-3 if x22 x2 find f(0) + g(T).…

A: We can find the answers as below.

Q: x² – 3x – 2 - if r<-1 x – 1 x + 3 f(x) = if - 1<x < 1

A: limx→-1-f(x)=limx→-1-x2-3x-2x-1=(-1)2-3(-1)-2-1-1=1+3-2-2=-22=-1

Q: Graph each function.

A: The zeros of a function are the point where the function value is equal to 0. These points are also…

Q: х+1 1. f(x) = х — 2 X - 1 2. f(x) = X-4 х+3 3. f(x) = х+2

A: As per our guidelines we are supposed to answer only first three parts. kindly repost others part as…

Q: 4-x 10. f(x)=- x+1

A:

Q: 2x + 5; if x 3 Find the value of functionf at x = 3.

A: Topic = Function

Q: Suppose f(x) = v9 +x - Vx – 6. Find all x-values satisfying the equation f(x) = 3. %3D

A: Given Data: Function: fx=9+x-x-6 Condtion: fx=3 Use substitution method to find the values of x for…

Q: 1. {(x) — х* -2х* +x —5 at x = 0 x+1 2. f(x)= х — 2 at x = 2

A: Given query is to find function is continuous or not at x= 2.

Q: f (x) = x* - 4x2 - x %3D as x -00 f (x) →-∞ as x -o f (x) → ∞ as x → +o0f (x) → -o0 as x +o f (x) →…

A: option (d) is  correct..

Q: x3 if x 1

A:

Q: f (x) = 2x² + 12x + 15 as x → -0f (x) → -∞ as x → -o f (x) → - as x → +0 f (x) → -0 as x →+o (x) → +…

A: Solve for the end behaviour

Q: x+4 2x - 3 x2 - 30 if x 5 Find: f(1) - (5) -

A: Given,

Q: 4. If f(x) = -2*43 find X-1

A:

Q: f (x) = - x + 43x - 5 %3D as x → -00 f (x) →-0 as x -∞f(x) -8 | as x +oof(x) → -8∞ as x → +of (x) →…

A:

Q: f(x) = (x-1)^3 (x-1) (x-2)

A:

Q: + x) at a = -2

A: The Taylor series of a function fx at a point x=a is defined as f(x)=∑k=0∞f(k)(a)k!(x−a)k where fna…

Q: 7.If f (x) = x³sinh(2x) then f'(x) = -1

A: Explanation of the answer is as follows

Q: x²-1 3. f(x) = -1;ƒ' (1) 2x+1

A: Solution is given below:

Q: 2. f(x) = x + 1 = 1 -1 :- x +1 8. 1(x) =

A: fx=x+1 take derivative f'x=ddxx+1 f'x=ddxx+ddx1 f'x=1+0 f'x=1

Q: (2x +1 if x<1 F(x)=1-2x +3 if x21 2. f(-2) = f(6) = f(1) =

A: Here we have to find the value of the given function at the required points. Initially we have to…

Q: Derivatives

A:

Q: x²+1 1 f(x) = X-1 f(x) = 1-x2

A: 1) Graph of f(x)=x2+1x-1 f(x) is well defined ∀x∈ R-{1} Domain (f) = R-{1} To graph the given…

Q: 2x-3 5. Let f(x) = find 3x+4 Ax as Ax -0

A:

Q: 2x-3 5. Let f(x) = find as Ax - 0 Ax 3x+4'

A: Given that: f(x)=2x-33x+4

Q: If f(x) = 3X, then f'(x)= 3TX A In 3 3TX B In 3 1(3Tx-1) D TIN3(3 )

A: We have to solve

Q: x-1 ifx1

A:

Q: find the value of f(-1) and f(3) y={3x+1      if x<3} {x^2      if x≥3}

A:

Q: x2 + 2/x + 3 If f' (x) = find the net change in f(x) between x=1 and x=3.

A:

Q: x²-1 for x1 -1+ 3. 2. 4.

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.