51. Find the left- and right-hand limits of the function f in Figure 2 at x = 0, 2, 4. State whether f is left- or right- continuous (or both) at these points. FIGURE 2

Q: Find the limit of f(x) = √(4 − x2) as x approaches −2 from the right.

A: We will find the limit by substitution

Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what…

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Q: Suppose f(x) = - 2x - cosr. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: Find the left- and right-hand limits of the function f in Figure 1 at x = 0,2,4. State whether f is…

A: At x=0, From the graph, as the point approaches x=0 from the left, the value of the graph reaches 1.…

Q: Can f(x) approach a limit as x ➔ c if f(c) is undefined? If so, give an example.

A: Yes .This statement f(x) approach a limit as x ➔ c if f(c) is undefined is correct. We will see one…

Q: If the limit of f(x) is 1 as x approaches 1 and the limit of g(x) is infinity as x approaches 1,…

A: we have to find the limit of the following

Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

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Q: Use limits to determine if f(x) = is continuous at z = -2. (z+2)²

A: Given that  f(x)= 1(x+2)2 is continuous at x = -2

Q: Determine the values of x at which the function in Figure 18 is: (a) dis- continuous and (b)…

A: (a) Here from the graph, we can see that, The graph has a break at the point x =1, that is, Thus…

Q: 3x 8 if x 7 x +5 Show that f() has a jump discontinuity at x = 7 by calculating the limits from the…

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Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

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Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

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Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

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Q: (a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

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Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: 2e What is the limit of the function f (x) = as x + xo ? 1-e

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Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

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Q: Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1+ (F(x))*. What is…

A: Given that f(g(x)). = x  and f'(x)= 1+(f(x))2 and we find g'(x). Here i attached solution of this…

Q: 3) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x).

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Q: Let 1 f(x) = x +3 Use the limit definition of the derivative to find the following. (a) f'(-7) = (b)…

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Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

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Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

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Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

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Q: -7 if x 2. Sketch the graph of the function and use the limit definition of the derivative to show…

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Q: Let f(x) = 1- 5x2. Use the limit definition of the derivative to show tl f'(x) = –10x

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Q: We can now evaluate this limit to conclude that the derivative is as follows. 1 a1/3 + a2/3) f '(a)…

A: We have to evaluate limit

Q: Find the following limits, where f is the function defined by (x +1 if x < -2

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Q: Look at the graph of the function f in Figure 1, f (−2), f (1), f (4) and D (f), then calculate the…

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Q: Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

A: To find limit of function f(x)=x2esin(1/x) as x approaches to 0. (Using Squeeze theorem)

Q: (B) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D

A: Explanation of the answer is as follows

Q: What is the limit of the function as x approaches -4 from the left? * (6,5) (14) (-4,2) *(6.2) -4 -2…

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Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

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Q: When a function's y-value approaches either +00 or -00 as x approaches c, the Limit Does Not Exist…

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Q: Let 1. f(x) x+1 Use the limit definition of the derivative to find (i) f'(-4) = (ii) f'(- 2) = (i)…

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Q: F:[- 2,2]– R, F(x) = L((- 3(² + 1) dt

A: We have F(x)=∫-2x2(t-3)(t2+1)dt       Apply Liebnitz's rule for differentiation under integration…

Q: Let f(x) = V5x + 2. Find the derivative f'(x) using the limit definition.

A: We have to find derivative

Q: Let f(x) be the function defined below. f (x) = Vx + 3 Use the limit definition of the derivative to…

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Q: 1. Explain what it intuitively means for function f(x,y) to be continuous in some domain D.

A: To explain the meaning of the given statement.

Q: Give the graph or the formula of a function that is continuous but not differentiable at x=0.

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Q: Which of the following does not represent a function that is continuous everywhere?

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Q: Find the limit as h approaches zero of f(x)=[1/(x+h)^2-1/x^2]/h

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Q: Start with g(x) = 3x. Use the limit definition of the derivative to show what g'(x) is.

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Q: _18. Determine the following function if continuous at f(x) = ) `x + 1' ; at x = 0

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Q: (i) Let ƒ be the function defined on (-o, 0) by f(x) = r$(3 – x)}. (2 – x) -2 Given that f'(x) = and…

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Q: 1 . Let f(r) 2r + 1

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Q: Consider the following piecewise defined function: Sr+5 | 4Vx +1 if x 2 3 if x < 3 f(x) = (a) Show…

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Q: Q4: Use the limit definition to compute the derivative, f'(x), for 2 1.F(x) = x3 2.F(x) = Vx³ – x

A: