Here is one more false claim and a bad proof. Claim C: Assume the function f is differentiable and that lim f(x) = 00. f(x) lim exists lim f'(x) exists "Proof": We can use L'Hôpital's Rule: f(x) f'(x) lim f'(x) lim lim lim 1 dr Explain the error in the proof. Then prove that the claim is false with a counterexample.

Q: is it true that ∇f(limx)=lim∇f(x) and further that ∇2f(limx)=lim∇2f(x)?

A: We know,  ∇f(xi)=f(xi)-f(xi-h), h=xi-x0i,i=0,1,2...And…

Q: 1 Use the definition of the derivative as a limit to find f'(x) if f(x)=- V9-x State the domain of…

A:

Q: * -x+1 if x1 (a) The value f(1) does not exist, while lim, 1 f(x) exists and equals 1. Doth f1).

A: f(x) = x3-x+1 if x<1        = 1/x        if x>1 Since the function f(x) is not defined at x= 1…

Q: Claim C: Assume the function f is differentiable and that lim f(x) = oo. f(x) lim exists lim f'(r)…

A: Note:- Before explaining the error in proof i'll show you counter example. it'll help you to under…

Q: 20. If f'(r) exists at r= a, then (A) True (B) False lim f(x) = f(a) PTA

A:

Q: 5. Use f(r) = r? - 3|r| to answer the following questions (a) Sketch an accurate graph of f(x) in…

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

Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

A:

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: If lim, 0 f(x) =o and lim, >0 9(x) = 00, then lim, »0[f(x) – g(x)]. OTrue False

A:

Q: using the definition of derivative f´(x)=limh-->0 (x+h)-f(x) /h enter the expresion needed find the…

A:

Q: (-ト-c)s x-5

A:

Q: True/False: If the domain of f(x) is all real numbers and f'(x) <0 for all x, then lim as x goes to…

A: Consider fx=e-x so domain is all real numbers.  Also, f'x=-e-x&lt;0.  Calculate the limit…

Q: How do I know that this statement is false? lim_x--> f(x) = L, then f(c)=L

A: Given statement limx-&gt;c f(x)=L, then f(c)=L

Q: True or false: lim(sin) as x goes to infinity exists.

A: Given, limx→∞sinx Find in the following that this limit is exist or not.

Q: Let sin(32) T f(x)=A, 5-√25- " x>0 x=0 x < 0. (a) Find _lim_ f(x) and lim f(x). (b) For what values…

A:

Q: Use the limit definition of the derivative to answer the following questions about f(x) = 8x².…

A: Given f(x)=8x2 We know that (a+b)2=a2+b2+2ab

Q: 1) The graph of a function y = f(x) has the line y = -2x + 5 as its tangent at the point (3, 10).…

A:

Q: Using the limits sin h lim h→0 h - 1 and cos h lim h→0 h - 1 as facts (which do not need to be…

A:

Q: If g is continuous at a and f (x)=(x² -a' )8(x). fir find f'(a). Hint: Use f'(x1) = lim S(x)-f(x,)…

A:

Q: True or False: The limit lim f'(x) does not exist. Explain your reasoning. True False

A:

Q: How close to 0 we need to take x so that lnx0 but f(0) does not exist

A:

Q: If (X, d_{1}) and (Y, d_{2}) are metric spaces, we define d: (X × Y ) × (X × Y ) \rightarrow R by…

A: Let X be a nonempty set with a mapping d:X×X→R is said to be a metric space if mapping d…

Q: Let F (x) = { tan (x − 3) x < 3 x-5 3 ≤ x Then lim F(x): x 3- = CH M₂ 146

A:

Q: sin(πx), x 1 For the function f (x) = a) Sketch the graph of the function. b) Evaluate limx--1-f(x),…

A: Given: fx=sinπx,x&lt;-1x,-1&lt;x&lt;1x,x&gt;1 for evaluating given limits, first we draw graph of…

Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: if f(x) True = False 1 {} if x # 0 if x = 0 2 then_lim ƒ(x) = 0 x 0

A:

Q: :N N amd 9: N-oN are functions such that f is not onto but f+9 is onto Prove that 9 is onto or give…

A: Suppose that f:ℕ→ℕ and g:ℕ→ℕ are functions such that f is not onto but f+g is onto. To prove that g…

Q: Let f(x) = 8x²+x+2. Then according to the definition of derivative (8(x+h)^2+x+h+2-(8x^2+x+2)) f'(x)…

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.