Exercise 1. Find the set S on which the sequnce of functions (fn)n Cconverges pointwise, and find the limit function. fn(x) = x"(1 – 2²).

Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: Given f(x) = xe¯²/2. Find the limit of f as x → +0 and x → -00. Find x- and y-intercepts and…

A:

Q: Express the limit as a derivative.

A: To express: limit limx→-1x3+1x+1 as a derivative. Concept used: Definition of derivative:…

Q: d) For the above function f(x), calculate the exact limit. e) Does the limit as x tends to 2 exist?

A:

Q: Consider the function f(x) given by the equation. f(x) = 2023 + 2022 + 2023 2021 + 2022 2021 2020 +…

A: We have to find the equation of the line tangent to the graph of f(x) at the point with x-coordinate…

Q: Nap Lajoie has a lifetime batting average of 0.338. Assume that Nap Lajoie came to bat officially…

A: Given : Nap Lajoie has a lifetime batting average of 0.338 and came to bat officially six times…

Q: x3 – 9x + 10 .lim 3 x→2 x2 – 4 4 |

A:

Q: Find the derivative Of 2x² usino efinition of The derivative -SPF pjest W

A:

Q: 1). Does the left-side limit of the difference quotient of the function g(w)=|w| exist at w=0? If it…

A:

Q: 1. Use the limit formula, and showing all work, find f'(x) for f(x) = -3x³ + 2x -1.

A: To find the differentiation of given function.

Q: 1. Let f(r) = 1– x². (a) Sketch a quick graph of f for -2 <r < 2.

A: The given function is The graph of the function is inverted parabola with vertex going in upward…

Q: 2) a) Recall that the definition of the derivative of a function f at a point a is given by f(a + h)…

A:

Q: The function f (x) is defined by the rule x2 +1 if x 2 - a) Calculate the left derivative and the…

A:

Q: Consider the function H(x): = 23 + 2x - 1 10x + 2 if x > 3 if x < 3 Determine if H is differentiable…

A:

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: x - 2 Evaluate f (x) = at x = 2. %3D X - 2 Select one: A. Continuous B. Discontinuous

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.