f(x) . If lim x→0 x? 1, find a. lim f(x) x→0 f(x) b. lim x→0

Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.

Q: Evaluate lim f(x) where f(x) = x +2 cosx +1 e-4 for x20

A: Use the existence of limit definition

Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: Given: limx→+∞ f(x)=4 limx→+∞ g(x)=3 limx→+∞ h(x)=-7 Find: limx→+∞ [f(x)+3g(x)] = ? limx→+∞…

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Q: Find functions f and g such that = 0 and lim g(x) = 0, but lim [f(x) – g(x)] + 0. lim f(x) :

A: Let assume two functions,

Q: f(x+h)-f(x) In evaluating lim h-0 in f(x)= x² -1, which is the first step? h

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Q: Find lim h(x), if it exists. X> 00 f(x) = 3x + 2x + 3 (a) f(x) h(x) = lim h(x) X> 00 f(x) (b) h(x)…

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Q: Evaluate the limit: lim (x - ln x)* x→0+

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Q: In evaluating 5 dx , is same as evaluating_lim_(in(f(x))). Determine the value of f(x) if x=4.6. -

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Q: lim (x 1/2 ln x) X→∞

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Q: Let f(x) = (1 + x)1/x. (a) Estimate the value of the limit lim (1 + x)1/x to five decimal places.…

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Q: Find two functions f and g such that lim f(x) and lim g(x) do not exist, but lim [f(x) + g(x)] * 0…

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Q: Using the definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the…

A: f(x)=2x3+10

Q: lim (sin?x x-0 x2

A: We use L-Hospital Rule to evaluate this limit.

Q: sin x – x (a) lim (b) lim (1+ x)/* 1/x

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Q: Prove the limit statements

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Q: Q.4: Prove or disprove, lim f(x) = 4 If f(x) = x # 2 x = 2' I-2

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Q: If f(x) < x² for all æ E R and lim f(x) exists, then what can be concluded about lim f(x)? a. lim…

A: we have to find the following

Q: lim (sec x)cot x X-

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Q: 2 ež h(x) 1 - 4 What is lim h(x)? x→+∞

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Q: Consider the function f (x, y) : 2y Show that lim (x,y)→(0,0) f (x, y) does not exist by ɛ – 8…

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: lim x→4fx = 0lim x→4gx = 0To verify:          lim x→4fxgx ≠ 0   is correct or not.

Q: 3. If f (x) = (x² – 1, if x 3 3.a) lim f(x) X-3 3.b) lim f (x) 3.c) lim f (x) X-1

A: The given function is f(x)=x2-1,if x&lt;3x+5,if x≥3

Q: Consider the function: f (x) · g (x) = 16x · sin What is lim f (x) · g (x)?

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Q: Evaluate the limit given

A: Given:

Q: neither lim f(x) nc

A: For the limit  fx and gx , take the condition . For function fx, fx=2 if x≥00 if x&lt;0 The limit…

Q: 1. Given that f (x) = -x² + 4x, and a = 2, find f(a + h) – f(a) lim h→0 h Explain the meaning of the…

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Q: ах Determine the values of a and b such that lim Vax +b – 3 = 5. x→0 bx

A:

Q: The cost of manufacturing a particular basebal cap is C(x) = 10,000 + 5x, where x is the number of…

A: Given that:

Q: x - 2x What is wrong with applying L'Hôpital's Rule to lim x+0 3x – 2

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Q: Find the limit. x² + y® sin х - у +7 lim (x.y)→(0,0)

A: Given,

Q: - Find the Lim;t: O Lim Sinx メー0 12ナメ3 E. 4) Lm sint2 sino lim 下-日

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Q: Given n ≥ 0;  explain that   limx→∞ fn(x)/(e^x) = 0.

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Q: Evaluate lim w/ e 1- sin C x)

A: First , evaluate the limit. limx→∞ex3−1sin1x=limx→∞ex3−1limx→∞sin1x=e∞3−1sin1∞=e∞−1sin0=∞−10=∞0…

Q: {x² +7, 14, x = 4 lim f(x), where f(x) =

A:

Q: x4/7 – 1 lim f'(a) where x→-1 x + 1 f(x) = and a = x4/7 lim x + 1 1 х>-1 II

A: Explanation of the solution is given below...

Q: Let f(x)=x'e* the value of lim [f (x) is: 4 x 1 a) 1 b) | e

A: Given   f(x)=x2ex2 We have to find 14limx→-1f(x)1x

Q: f(2) is continuos if lim f(z) =f(z,)

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Q: a. Graph h(x) = x2 cos (1/x3) to estimate limx--&gt;0 h(x), zooming in on the origin as necessary.…

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Q: Find the limit. sin(x) – 9x lim x+00 x+xe-x

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Q: Given: f(x) = 4 –x’ and g(x) = Vx+1 a. lim f(x) =

A: Given, fx=4-x2gx=x+1

Q: 45. a) Find lim h(x). b) Find h(1). c) Is h continuous at x = 1? Why or why not? d) Find lim, h(x).…

A: Given Example -

Q: b. Is lim (x sin x) = lim f(x)g(x) = lim f'(x) lim gʻ(x) = ( lim 1)( lim cos x) = 1 a true or false…

A: Let we need to determine this limitlimx→0(xsinx)

Q: f(x+h. f'(x) using the definition lim h-0 O 26x + 30 O 5z + 13 O 5x O 10x + 13 O 10z

A: for the function f(x)=5x2+13x+30 find f'(x) using the definition limhf(x+h)-f(x)/h 26x+30 5x+13 5x…

Q: 2 dx In evaluating is same as evaluating lim cosF(x))lc. Determine the value of f(x) if x=3.22 xV x2…

A: Solve the

Q: Evaluate the limit sin 2x lim z+0 9x

A: Answer and explanation is given below

Q: Given that lim f(x) = 2 ,lim g(x) = -4 ,lim h(x) = 0 %3D %3D xa xa Find the limit lim[h(x) –…

A: Limit evaluation: 1) limx→cA(x)+B(x)-C(x)=limx→cA(x)+limx→cB(x)-limx→cC(x) 2)limx→aag(x)=alimx→ag(x)

Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

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Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

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Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

A: