(a) Prove that, (i) lim = 0 (ii) lim = (0 (b) Using (a), prove that the function f(1) = on (0, + 1) has an absolute maximum. (c) Find that absolute maximum.

Q: (x+ h)- f(x) In Exercises 26-27, find lim- 1-x (x) =- 26. X+2 27. (x) = Vx - 3

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Q: [x2+3x-1 a. lim 1 6 b. lim X+2 Lx-2 x2+2x-8 E. lim - h-0 h x+h Vx+h-Vx d. lim x >0 h-0 h

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

Q: Determine whether the function x2 + 2 x > 2 f(x) = x = 2 is continuous at the 4х — 2 x < 2 given…

A: First of all we will find the left hand limit at X equal to 2 and then find the right hand limit X…

Q: 1. Use your knowledge of graphs of functions and their derivatives to find the value of lim Show…

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Q: (-금x+ 2, x 0 exist? If yes, give its value. If not, why?

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Q: V1 +x - 1 Find the limit lim x-0 if it exists.

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Q: 4-x V6-5x+x f(x) = 1- find the domain 2- find lim f(x), lim f(x), lim f(x) x2 x-2 x-+2

A: givenf(x)=4-x2x2-5x+6solving x2-5x+6 by factorization method=x2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)and…

Q: x2 +1 Can L'Hôpital's Rule be applied to lim x→1 2x + 1

A: To check if the L'Hospital's Rule can be applied or not, first we need to find the limit by directly…

Q: Consider the function Pue au Marka 1- x2, x1 f(x) = 2, %3D X = 1 Graph the function f(x). Find…

A: (Since it is not mentioned which question to solve and question 4 part 2 is not clear so Solving the…

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

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Q: Find the limit, if it exists. (x² – 16 if x>0 Let f(x) =x2 -16 if x<0 x- 4 Find lim f(x). x-0- 00 -4…

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Q: x² - 4x-5 x-5 x² +6x + 8 x+2 13. What is the limx-5 14. What is the limx→-2 15. What is the limx-…

A: Since you have posted a question with multiple we will solve the first question for you. To get the…

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^-?…

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Q: lim f (x) = DNE f(x) has a vertical asymptote at x=3 x-3

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Q: 5. Find lim f(x) f(x) 2 1 i -1 2 -2

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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: x²-4 How come lim x-2 x-2 cannot be evaluated using the quotient limit law? How come lim Vx – 2…

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Q: 1.1 Explain the difference between an accumulation point and a limit. 1.2 If lim a, = x and lim yn =…

A: Solution a: Difference between Accumulation point and Limit point: Since accumulation point is the…

Q: 1. Determine whether the function f(x) = x2 + 6x + 9 is continuous at x =-= Sketch its graph…

A: Consider the provided function and the point, fx=x2+6x+9,   x=-2 Evaluate the provided function at…

Q: x² + x – 6 - f. lim "3 x² – 9 /x + 1 – 2 g. lim х — 3 * 3 x - 8 h. lim * 2 2 x- 2 3x2 + 5x - 2 i.…

A: Given tha

Q: (e) limVx ) lim -+(-1)") X-00 n→0 n n²-12345 x2 +9 (g) lim n +1 (h) lim x∞x3 +1

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Q: a) b) c) -4 -3 -2 -1 lim f (x) x-1 lim f(x) X→-2 lim ¿ x- 2*¹ f (x) ¿ f(x) LO 4+ 3- 2+ 1- 0 H -2+ 1…

A: Given that a graph and we find given limits - a) lim(x tends to 1) f(x). b) lim(x tends to -2) f(x).…

Q: Let f(x)= -6x^4+8x^3+72x^2 a) f has a relative minimum at x= b) f has an inflection point at x=…

A: Given; Let f(x)= -6x4 +8x4 +72x2   a) f has a relative minimum at x=

Q: The limit of the function lim x → − 2 ( 2 − | x |/ 2 + x )

A: Here we have to find the value of limit limx→-222-x2+x

Q: When the function f(x) satisfies f(1) =1,f'(1)= 3 obtain a value of lim/ (2)" -1 x→1 x² – 1

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Q: x*-4y2 Find lim (x,y)¬(0,0) x2+2y2 if it exists, or show that the limit does not exist.

A: The given limit limx,y→0,0x2-4y2x2+2y2

Q: (a) lim 47:17 Sx 3x-14 1. Find the limit:

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Q: 1 Let f(x) =. 1,0sx<2 .Determine lim f(x) -x² + 4x – 3, x 22 X2+

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Q: x2-x-6 lim x-2 x2-4 Vx+2-2 lim x-2 x-2 Vk+3-V3 lim k-0 k

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Q: Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999,…

A: First, we factor numerator and denominator. Then we simplify for x not equal to 3. Then use this…

Q: a) lim- 1 3x +x+1 -x +5x b) lim f(x) where f(x)={ (4x xs2 3x x>2 sin 2x c) lim g(x) where 2+x < g(x)…

A: alimx→∞−x2+5x3x2+x+1Divide and multiply by x2limx→∞x2−x2+5xx2x23x2+x+1x2limx→∞−1+5x3+1x+1x2=−13

Q: 1. Find a) lim x+3 3-x b) lim x3* 3 - x c) lim- +3 3-x d) the vertical asymptote of f(x)= 3-x

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: f(x)=(1-2x)/x, find lim f(x) approaches 3 and limit f(x) approaches 4

A: Given that the function is,

Q: lim f(x)=+0, then the limit lim [2² . f(x)] .. If must be equal to zero. must be equal to +00. must…

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Q: 1 1 +x+1 h 4 (a) Lim (b) Lim h-0 V5h + 4 –- 2 5 t3 – 1 (c) Lim- = 3. t-1 t- 1 II

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Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

A: Solution. :

Q: 1. Sketch a graph of a function f(x) with the following properties: f(-2) = 0, ƒ(2) = 0, lim_f(x) =…

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Q: 2x + 4 h(x) = 1 2x 1 f (x) = 1 –x g(x) = 3( x + 2x 6. | 3 -- 8. a.lim -4 · f (x) d.lim (8 · f(x) –…

A: Given:      fx=1-18x      gx=3x+2x6+4     hx=2x6-2x+13

Q: 49-7 Estimate lim *-7 -7 is approaching to using a table of functional values.

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Q: g) Y2-Y1 X2-X1 h) f(x+h)-f(x) (x+h)-x i) lim-0 f(x+h)-f(x) (x+h)-x i) lim-0 f(x+h)-f(x) (x+h)+x

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Q: x² - 5x – 24 lim Calculate the limit: x-3 x+3

A: the given limit is: limx→-3x2-5x-24x+3 we have to evaluate the given limit.

Q: A function is a ratio of quadratic functions and has a verticalasymptote x =4  and just one…

A: Given: A function is a ratio of quadratic functions. Vertical asymptote at x =4. x -intercept: x =1…

Q: 13. (a) Estimate the value of lim- X x+√1+3x-1 X √1+3x-1 By graphing the function f(x) = - (b) Make…

A: Given: 13. f(x)=x1+3x-1 To find: (a) Value of limx→0x1+3x-1 by graphing f(x)=x1+3x-1 (b) A table of…

Q: 1. Find a) lim x3 3-x b) lim x+3* 3-x c) lim- x+33-x d) the vertical asymptote of f(x) =- 3-x

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

Q: 1. Evaluate lim (2x-5) given its graph below. X-2 b. -1 c. 2 d. 1 а. О 2. Given the graph of f(x)…

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Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

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Q: 1- let f(x)= |x^2-4|/(x+2). Determine the limit lim_{x->-2} f(x), if it exist.

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

Q: 1. Shows that the function f(x): x2+2 Lis continuous at x = 0, but has jump discontinuity at x-3 x=…

A: 1. f(x)=x2+2x-32. f(x)=x2-9x-33. limx→-12x2-ax-14x2-2x-34. f(x)=x2-xx-1

Q: 13. |z| lim -1 -0.5 -0.01 -0.0001 f(z) 1. 0.5 0.01 0.0001 f(x) What is the value of the value of…

A: Topic- limit