Let f(x)={−5+x,ifx<31−x,ifx≥3f(x)={−5+x,ifx<31−x,ifx≥3 Evaluate the following expressions. limx→3−f(x)= limx→3+f(x)= f(3)= Is the function ff continuous at 3?

Q: Find the limit of f(x) = √(4 − x2) as x approaches −2 from the right.

A: We will find the limit by substitution

Q: Prove the limit statements

A: The given function is To prove

Q: Find the limits x2/3 + x1 lim X00 x2/3 + cos?x

A: Given: The function is f(x)=x2/3+x-1x2/3+cos2x   To determine: limx→∞ x2/3+x-1x2/3+cos2x

Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: Find a value for the constant "a" that will make the function f(x) continuous. f(x) = { ax- if xs2…

A:

Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

A:

Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

Q: Find the value of the limit below. [4 – 6(x + Ax)]? – (4 – 6x)² - lim Ax → 0 Дх Specify the function…

A:

Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

A:

Q: lim 4 sin(x + n) + 3

A:

Q: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: Let f (x)=x²-2x + . Find the slope of the graph y = f(x), at point P- (0,7) evaluating th'e limit AX…

A: fx=x2-2x+1 We need to find the slope of the graph at the point P0, 1

Q: Suppose that a function ƒ satisfies the following two conditionsfor all real values of x and y:i)…

A:

Q: Find the following limits: Vx+3-1 i. x-2 x+2 lim 1 + x-1- \]x-1| ii. lim x2 +3x, Vx+-7 lim X→+co…

A:

Q: If 3x 2 s f(x) s x² - 3x +7 for x 2 0, find lim f(x). x3

A: Given:  3x-2 ≤ f(x) &lt;= x²-3x + 7 for x ≥ 0

Q: (fif2..f)is di fferentiable at x, proofthat ... by using f(x)– f(*.) f (x)=lim, x-x,

A:

Q: 3. Can f (x) approach a limit as x → c if f(c) is undefined? If so,

A:

Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

A:

Q: Let lim,-0+ f(x) = -2, where 8r - 3 for r <0 f(x): | 4x – 2 for r2 0 f(r) = Then what is (the…

A:

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 2x + 7 x3 – x² + x + 7 f(x)

A: Given that, f(x)=2x3+7x3-x2+x+7 Factoring out x3 on both numerator and denominator we get,…

Q: d) lim f(x), where x-2+ (x² + x + 1 if x 2

A:

Q: Find the values of k that make the function continuous. Jk² + 18x, x > -3 f (x) = kx, x < -3

A:

Q: Find the Limiti lim (xt +2x") メ→ -○

A: Solution is given below

Q: 3) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x).

A:

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: 15. If f(x) = x2 - 6x - 9, find f(x) by using the formula/limit definition of derivative.

A: Given: fx=x2-6x-9 we know that derivative for any given functionfx by using limit definition is…

Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

A:

Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

A:

Q: Q2: Find the limit x + 3 lim x→-3 x2 + 4x + 3

A: We have to find limit

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

A:

Q: If 3x – 2 s f(x) < x² - 3x + 7 for x 2 0, find lim f(x). X3

A: 3x-2≤f(x)≤x2-3x+7

Q: Find the limit L. Vx - 3 1 lim X 4 X- 4 L =

A: After the substitution of limits the function gives an indeterminate form 00.

Q: Q2/Give a value for each of the following limits: x2 - 4x – 21 1) lim 7 3x2 - 17x – 28 (7+2x)-V5-vZ)…

A:

Q: Given f(x)= x² and  g(x)= 4x+1 if x>2          = x²+5 if x≤2 a)use the limit definition of…

A:

Q: Find the value of the constant c such that the function f(x)= (x-2)/( (root 4x+1)-3) if x#2, c if…

A: And

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Find the value of the positive constant c such that....

A: Given- limx→∞x-cx+cx=14 To find- The value of c. Concept Used- If any limit of the function fxgx in…

Q: (B) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D

A: Explanation of the answer is as follows

Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

A:

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: If 2x - 2s f(x) S x² - 2x + 2 for x 2 0, find lim f(x) x-2

A: see below the answer

Q: Q.4: Prove or disprove, lim f(x) = 4 If f (x) = } x # 2 x = 2 x→2 2.

A:

Q: If V5 - 2r s f(x) < V5 - x for -1 sxs 1, find lim, 0 f(x).

A: Given: 5-2x2≤f(x)≤5-x2

Q: Given f(x) = 4 – 3x, find f'(x) using the limit - definition of the derivative. f'(x)=

A: The given function is:fx=4-3x2To find f'x

Q: Let f(x)=4x2 +6. Evaluate limh→0f(4+h)−f(4) / h Limit =

A:

Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: Find the limit as x approaches negative infinity of (xe1/x-x)

A:

Q: f(x) = 3x 2 − 2x + 1.

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.