If (an) has a decreasing subsequence, then (an) does not tend to infinity.

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

Q: There is a jump discontinuity at x = 1 and lim f(x) = 1

A: At X=1, there is a jump discontinuity.   limx→1- f(x) = 1.As function f(x) approaches towards 1 from…

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: R(x) 16 14 12 10 6. 4 2 3 4 Years Revenue (millions of dollars)

A:

Q: Suppose g is a continuous DECREASING function on the interval [-3,1].

A: 2. As y is a continous decreasing function on the interval -3, 1

Q: Find the limit of the square root of (4x^(6)-x) over (x^(3)+3), as x approaches positive infinity

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Q: Find the slope of the tangent line to the graph of f(x) = x³ + x at x = 3 using the limits…

A: Given- fx=x3+x To find- The slope of the tangent line to the above function at x = 3 using the…

Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

A:

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

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

A:

Q: (х — 2)(х + 2)(г+ 1) (г + 3)(ӕ + 1)

A:

Q: given f(x)=x^2-2x use the limit defintion of derivative if f'(-2)

A:

Q: Find the limit of f(x) = v9 – x² as x approaches -3 from the right.

A: follow next step

Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

A:

Q: .Find the Global Extrema for f(x) = Bx4-BeB-A)x. Use the second derivative to determine if those…

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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: for f(x)=x^2-1 find f(2) using the limit definition of the derivative

A: The limit definition of f'(a) is:f'(x)=limx→af(x)-f(a)x-a

Q: Find the slope of the graph of the function g(x) = (5x)/(x-2) at (3,15) using the definition of a…

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Q: find the limit of x^2/1-4x^2 as x approaches infinity

A:

Q: In terms of limits, what does it mean for f to grow fastet than g as

A: We have to express that 'f grows faster than g as x→∞' in terms of limit.

Q: Find the limit as x approaches 3 for x²-3x 2x²-5x-3

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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: ) Use the limit definition of derivative to compute k'(x).

A:

Q: Give the formula for a function which has vertical asymptotes at x=7 and x = -6 but is otherwise…

A: A function has vertical asymptotes at x=7 and x=-6 but is otherwise continuous.

Q: Find all points on the graph of F(x)=-x3+3x2-2 at which there is a horizontal tangent line.

A: Given curve is Firstly, we will find derivative of F(x) We now that slope of tangent to a curve…

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Find the slope.

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: Use the definition of the derivative f'C)=lim flxty-PG4. to compuke derivative of flx)= 3X-X

A:

Q: Find the limit of the function (2x ^ 2 - 4x)/(x + 1) as x increases without bound

A: find limit as 'x' increases without boundlimx→∞ 2x2-4xx+1

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: Consider the given function as fx=100x,and gx=xx

Q: Use the derivative ƒ' to determine the x-coordinate of the local maxima and minima of ƒ, and the…

A: We have the derivative as ƒ'(x) = (x - 1)(x + 2)(x + 4) put f '(x)=0   so,  x=1, -2, -4 sign of f…

Q: Which of the following functions has a horizontal asymptote at y =-?

A: Here, the objective is to find the horizontal asymptote of the function.

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

A: We have to find derivative

Q: Given that f(x) = 4x2 − x + 2, use the limit definition of the derivative to compute f'(x).

A:

Q: sketch the graph of a function that is continuous everywhere except at x=3, and is continuous from…

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Q: Find the limit of the function, f, as x approaches – 3. x2 – x – 12 - - f(x) = x + 3

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Q: Find the limit of f(x) = 9x+9/8x+8     as x approaches infinity and as x approaches negative…

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Q: Find the limit f(X) as x approaches -1 from the left.

A: Graph of f(x) is continuous at x=-1 and f(-1)=2 hence limit f(x) approaches to 2 as x approaches to…

Q: Does the limit of a function depend on how the function is defined at the point being approached?

A: We know that, For the limit of a function to exist at a point, the functional values must approach a…

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: The slope of the tangent to the graph 13−x2 by the limit definition.

Q: Sketch the graph of an increasing function such that f'' (x) changes from + to − at x = 2 and from −…

A: Sketch the graph of an increasing function such that f”(x) changes from + to - at x = 2 as follows.

Q: Which of the following has a horizontal asymptote of y = 0?

A: In all given option

Q: Find the horizontal and vertical asymptotic for f(x)= 1/(1-x^2)

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Q: Let f(x) = 2x2 +1. Use the limit definition of the derivative to find f'(x).

A: We can find f'(x) Using following formula

Q: what is the limit of x minus the square root of x, as x approaches infinity

A: Given,

Q: (х — 2)(г + 2)( +1) (х + 3)(ӕ + 1)

A:

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

A:

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: The slope of the tangent line m to the graph of fat the given point x0,fx0 is expressed as-…