Description lim f(x) Find where J is the function defined by 1-x if x < 0 f(x) = (x)3D 1+x 2 if x > 0 x+2

Q: LIMITS of a FUNCTION Evaluate the followinci limits. 2-Vx 3. lim, 4-x x - cos X 4. lim,

A: 3. To evaluate the limit limx→42-x4-x Solution We know that a2-b2=a+ba-b. Evaluating the limit.…

Q: sin(3x) Evaluate the limit : lim Show x→0 2x + x3 your work.

A:

Q: 5. simple limit of positive definite function is also positive definite function. p(x) = lim ,(x)

A: Solution :-

Q: Limits of Average Rates of Change Because of their connection with secant lines, tangents, and…

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Q: Determining limits analytically Determine the following limits. x* - 5x lim xS0 x2

A: To evaluate ,limx→0 x3-5x2x2

Q: Proof Prove that if lim f(x) = 0, then lim f(x)| = 0.

A: Given that to prove if limx→c f(x)=0, then  limx→c f(x)=0Now,

Q: lim f(x) Find x-2 lim f(x) and x-2*

A: We have given the graph. now using it we have to find left hand limit and right hand limit at x=2.

Q: Existence of a Limit Determine whether lim f(x) exists. Explain. lim f(x) = 1 and lim f(x) = 1 x→3-…

A: Consider the given limits limx→3-fx=1 and limx→3+fx=1   Limit of fx at any value of x, say x=c…

Q: Uniqueness of limits Show that a function cannot have two differentlimits at the same point. That…

A: Suppose fx:K→ℝ and c∈ℝ is a limit point of K⊂ℝ.Assume limx→cfx=L1limx→cfx=L2Where L1, L2∈ℝ

Q: . Chain Rule Suppose that f(x) - * and g(x) - |x|. Then the compositions (f• g)(x) - |x| - and (g…

A: Let  f(x) = x2 and g(x) = x.Then      (f∘g)(x) = x2…

Q: sin x 84. lim

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Q: Test II: Evaluate lim (x+h)-f(x) solutions) for the given function f (show h-0 5. f(x)=

A:

Q: (x^3-x^2) divided by (x-1) lim x-> 1 Evaluate the limit.

A: GIVEN: limx→1 x3 - x2x - 1

Q: Domain: x* lim f(x) = x3 lim f(x)= x-3- lim f(x) x-3+ lim f(x) = f(0) = f(x) = 0= x3D}

A: (a) From the given graph of f(x), When x approaches 3 from the left and from the right, y approaches…

Q: Finding the Derivative by the Limit Process InExercises 1–4, find the derivative of the function by…

A: Given function is: f(x) = 12 We have to find the derivative of f(x) using the limit process.

Q: One-sided limits a. Evaluate lim Vx - 2. xS2+ b. Explain why lim Vx - 2 does not exist. xS2-

A: We know that a function fx=x is defined if x≥0. a. We have to evaluate limx→2+x-2 Here x→2+ it means…

Q: Limit Evaluate lim (tanh x)*.

A: Consider the given: limx→∞ tanhxx Apply exponent rules:limx→∞ tanhxx=limx→∞ exlntanhxApply limit…

Q: One-sided limits x - 3 a. Evaluate lim xS3- V 2 - x b. Explain why lim. 3 does not exist. xS3* V 2 -…

A: Given: limx→3-x-32-x for evaluating given limit, we substitute value of x=3-

Q: sinx 4x lim lim(1 + 3x), [x² -4 Is the function f given by f(x) ={ x-2 x* 2, continuous at x= 2? Why…

A:

Q: limits at infinity x – 19x° + 30x4 'x→∞ -6x² +x³ - 8 Compute lim. Show every step and use proper…

A: Solution: The objective is to compute the given limit

Q: Creating functions satisfying given limit conditions Find a function f satisfying lim - f1x2 2. xS1x…

A: Consider the function fx=x2-1. Now check the limit as follows.

Q: Lim x -&gt; 2 (x^2-1/x-2)       The lim x --&gt; 2 is both negative and positive.  i dont remember…

A: Given:

Q: Evaluating Limits Use a graphing utility to evaluate tan nx lim for several values of n. What do you…

A: Consider the provided limit, limx→0tannxx Use the graphing utility find the limit and put the…

Q: Determining limits analytically Analyze the following limits. 2 - 5x 2 - 5x a. lim xS3* x - 3 b. lim…

A: Given: The expressions of limit as a.limx→3+2-5xx-3 b.limx→3-2-5xx-3 To find: The limits…

Q: Estimating a Limit Consider the function x + 1| - |x – 1| f(x) = Estimate |x + 1| – |x – 1| lim -…

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Q: Lim cot(3X cotlôx) X- 3

A:

Q: Derivative information Suppose a continuous function ƒ is concaveup on (- ∞, 0) and (0, ∞). Assume ƒ…

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Q: Test II: Evaluate lim 7*+h)-/ for the given function f (show f(x+h)-f(x) h→0 solutions) 2. f(x)=…

A: we can find limh→0f(x+h)-f(x)h for given f(x).

Q: lim x approaches infinity x1/x

A:

Q: Determining limits analytically Determine the following limits. lim csc x xS0-

A: we have the limit limx→0-cscx

Q: lim x-> sin3xcot4x/cot5x

A: We have given the limit function;

Q: lim x -> 0 ((sin(3x)) divided by ((tan(3x)) Evaluate the limit.

A:

Q: 16 6e4x _e-2x lim x→-∞ 8e4x-e2x+3e¬x X→-00

A:

Q: Left- and Right-Hand Limits Not Equal Investigate the one-sided limits of f(x) = as x → 0. Does lim…

A: Left hand limit: Right hand limit:

Q: Limit and Continuity Find the limit (if it exists) and discuss the continuity of the function.

A: We have,

Q: lim x* Evaluate the limit:

A:

Q: Calculating limits Determine the following limits. lim 11x - 11 + x2 and lim 1x - 11 + x2 xS-

A: Given, limx→-∞x-1+x     and    limx→∞x-1+x

Q: Limits of functions of three variables Evaluate the following limits.

A: Evaluate: limx,y,z→1,1,1yz-xy-xz-x2yz+xy+xz-y2

Q: 7. lim f(x) = -00, lim f(x) = 0, lim f(x) = 0, %3D x→ーの lim f(x) = 0, lim f(x) = - it

A: I have sketched the graph of each function

Q: LIMITS of a FUNCTION Evaluate the followina limits. - 4| 1. lim, X- 2

A: Let,f(x)=limx→2x2-4x-2Put,x=2 ,=limx→222-42-2then, the limits take 00 formNow,using L-hospital…

Q: Finding the Limits Based on Graph Find the limits of the function as given in the graph: lim f(x) 1.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: uestion 5 ( ) Algebraically show that f(x) = 5x2 + 2, x <0 is one-to-one and find f-).

A:

Q: Long Term Behavior of f What is the value of limf'(x)? What does the value of this limit tell you…

A: We have to deduce from the condition if lim x tends to +♾ f '(x) = a. If a = 0, then the function…

Q: Limit and Continuity Find the limit (if it exists) and discuss the continuity of the function.

A: Find the limit (if it exists) and discuss the continuity of the function.

Q: lim f(x) = x→6.2+ lim f(x) = x→6.2¬ At the point x = 6.2, the function is %3D right-continuous only.…

A: The function is,   The limit of function f(x) from the right of 6.2 is,

Q: calculus help Find and classify the local maximum and minimum values of g(x) = e(x^3/12)-x using…

A: Given:Here g(x)=ex312-xTo find:The local maximum and minimum values

Q: Limit of a difference quotient Assuming ƒ is differentiable forall x, simplify

A: Here given as L=limx→5fx2-f25x-5 When the limit applies, It becomes 00 form. Thus use I'hospital…

Q: Determining limit analytically (use algebra): limθ→π2−cosθsin2θ−1.

A: