A function f is differentiable at a number a You Answered if f is continuous at a. f(x)- f(a) if lim Correct Answer exists.

Q: نقطة واحدة If a function is continuous .7 at a point, then its first * derivative may or may not…

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Q: 4 3 2 1 -5 -4 -3 -2 -K 2 3 4 5 -2 -3 -4 -5

A: Function to be continuous, peak value doesn't affect the continuity. Hence f is not continuous at…

Q: HOSPitars fule lim X->0+ ex-1 Hx

A: Given that limx→0+1x-1ex-1Solution :limx→0+1x-1ex-1limx→0+ex-1-xxex-1Applying L hospital…

Q: The limit represents a derivative f'(a). Determine f(x) and a. 9h lim 1 h→0 (Express numbers in…

A: The limit represents a derivative f'(a). We have to determine f(x) and a .

Q: 1. If lim f(x) = 5, which must be true x →2 I. f is continuous at x = 2 II. f is differentiable at x…

A: The given limit is: limx→2fx=5 That means, left side limit and right side limit at x=2, tending to…

Q: 4. Determine whether the functions f are continuous at given points: x+2 S(x) ={ x +x-2 0, x=1 at x…

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Q: The limit represents a derivative f'(a). Determine f(x) and a. 11 1 lim h-0 (Express numbers in…

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Q: The limit represents a derivative f' (a). Determine f(x) and a. 6h lim 1 h→0 h (Express numbers in…

A: We have to find

Q: Find the values of the constants c and k that the function make lim f (x) and lim f(x) x-2 X-1…

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Q: (a) A function is continuous from the left at a if (b) A function is continuous from the right at a…

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Q: 10x3, 5-x, = x < -2 x ≥ −2 Let f(x) 1. f(-2)= 2. lim f(x) = x→→2+ 3. lim f(x): = x→→→2 4. lim f(x) x…

A: The solution of 4 and 5 are given in the next steps.

Q: The exponential functions f (x) = a* (a > 0) are continuous on the interval (-00, ∞). Use this fact…

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Q: ((x + 3)2;x 1 f(x) = %3D 1. lim f(x) = x--5- 2. x→-5+ lim, f(x) = %3D 3. lim f(x) = %3D x--5 4.…

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Q: 1. True or false. (a) For a differentiable function f, f'(x) gives the slope of the tangent line at…

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: 6 (а). Let f be a differentiable function with f(0) = 1, f'(0) = 2. f (x)+f(2x)+ f(3x)- 3 Find lim

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Q: lim f (x) where f (x) = x 1

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Q: f(x) x f'(x) f”(x) f"(x) 2 0 0 5 7 The third derivative of the function f is continuous on the…

A: Given: The values of function and its first three derivatives at x=2 are given in the picture below:…

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…

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Q: 6 (a). Let f be a differentiable function with f(0) = 1, f'(0) = 2. f(x) + f(2x) + f(3x) - 3 Find…

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Q: 5.4.3 DEFINITION (Area Under a Curve) If the function f is continuous on [a, b] and if f(x) > 0 for…

A: The solution are next step

Q: Create an example of a function f, such that f(3) and lim f(x) are both defined and yet have…

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Q: Example Let f(x) = /x. 1. Find f (x) using the (limit) definition. 2. Find f'(4). 3. Find the…

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Q: tan(ëx) – 1 The limit lim represents a derivative f'(a). х — 1/4 x-1/4 (a) f(x) =. a =. (b) Find…

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Q: The limit represents a derivative f' (a). Determine f (x) and a. 6h lim h 1 h-0 (Express numbers in…

A: find fx and alimh→06h-1h

Q: f (x+Ax)-f(x) f'(x) if f(x) =- x by applying f(x) = lim Ax-0 Ax

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Q: The graph of a function f is given. Determine whether f is continuous on its domain. continuous not…

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Q: Consider the function: f(x) = x³ - 5 i. Use the limit definition of the derivative (First…

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Q: x² if x >0 if x <0 3. Consider the function f(x) 3D Find lim f(x) if it exists or state it does not…

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Q: Sketch one possible graph of a function f(x) defined on R that satisfies all the listed conditions.…

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Q: 4. f(-5) = 5. Is the function continuous at x = -5? If not, what type of discontinuity occurs? 6.…

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Q: 3+ x if x < – 1 Let f(x) ={ x² if –1sx<1 2- x if x 21 a) Evaluate (i) lim f(x); (ii) lim f(x); (iii)…

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Q: The limit represents a derivative f'(a). Determine f(x) and a. 8h lim h 1 h-0 (Express numbers in…

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Q: 1. Consider the function f(x, y) = 2y (a) Show that lim (x,y)→(0,0) f (x, y) does not exist by using…

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Q: so lim f(x) = Also, f(1) = Thus, fis continuous at x = 1. We conclude that f is continuous on (-∞,…

A: We first find the left and right hand limit

Q: The limit represents a derivative f'(a). Determine f(x) and a. 8h lim h - 1 h→0 (Express numbers in…

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Q: A function y = f(x) is defined and continuous for all x. This function satisfies all of the…

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Q: f. lim f(x) if f(x) = |x² – - 2 if x > -1 1/x g. lim f(x) if f(x) : if x -1 x +3 if x 1

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Q: lim f(x) and lim f(x), where メ→0 -x+1 ifx0

A: The function is given as fx=-x+1    if x≤02x+3     if x&gt;0 find limx→0+fx and limx→0-fx

Q: x 0 Can also be displayed as: f(x) = [x - 1 when x < 0, 1 when x = = 0, x² 1 when x ≥ 0] For this…

A: The given function,     fx=x-1,x&lt;01,x=0x2-1,x&gt;0

Q: The value of lim (/x+1-/x) is the same 1 A lim x- ol x +1 +/x B lim (Vx+1+/x) lim (Vx+1+/x) (D None…

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Q: lim f(x) exist, then exists .a is a constant function .b is a continuous at x = c .c lim f(x) =…

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Q: A function y = f(x) is defined and continuous for all x. This function satisfies all of the…

A: It is required to understand the question properly and then graph the function.

Q: f(x+h)-f(x) to For f(x) = use the definition of differentiability f' (x) = lim- %3D (x-1) determine…

A: Given: The function fx=x2x-1 To determine: The differentiation of fx at x=1 if the function is…

Q: Find f(x + h) Find f(x + h) - f(x) Find (a+h)-f (æ) h Find lim f(x+h)-f(æ) as h → 0

A: Given:f(x)=3x2-4x+7

Q: 2) Let f be a piecewise-defined function given by: (4 log,(x) + VAx -8 3 sin(x) +2 if x>3 f(x) = if…

A: solution:-f(x)=4log9(x)+4x-83sinπx+2x,     if x&gt;312,                             if…

Q: The limit represents a derivative f'(a). Determine f(x) and a. 104 – 1 lim h→0 h (Express numbers in…

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Q: A. Find the limits of the function f(x,., -2 2 1. lim f(x)= x--1+ 2. lim f(x)= X-4- 3. lim f(x)= 4.…

A: The graph of the function is  To evaluate:  1. limx→1+fx2. limx→4-fx3. limx→4+fx4. limx→1-fx5.…

Q: 2. a). Determine the interval (s) on which f(x) = 1 is continuous. b). Find lim analytically (use…

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Q: The derivative of a function f(x) 93 the function defined by the following limit flxth)-8しx) lim…

A: Given:- f(x)=4x2 To find:- f'(x) by using limit definition