QI. Let f: (0, a] R be a function such that f(x) = x has a limit at a. If f is defined at a , where the value of & exactly is A. E В. Е C. 2a D. 3a Q2. Let f:R-R be a function such that f(x) = x sin f is defined at xo, where the value of & exactly is has a limit at xo 0. If A. E B. E- Xo C. e+ xo D. Xo

Q: Q2. Let f: R → R be a function such that f(x) = x sin f is defined at xo, where the value of 8…

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A: Topic- Limits

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Q: If c is a constant, what is the limit of c as x approaches a? 0 C a X

A: A detailed solution is given below.

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A: key point 1) limit is path independent

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A: We will plug the limits in function to find limit of function

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Q: 1. Prove the following limits xy lim (x,y)→(0,0) √x²+y² x³+y³ D) E) lim (x,y)→(0,0) F) x²+y² x² - y²…

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Q: Given that f(x) = e ,which of the following is equal to the limit F(; + h) – f(}). lim h→0 ? h Oe…

A: From definition of derivative we know for a function f(x),  limh→0f(a+h)-f(a)h=f'(a)

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Q: Evaluate the limit of the function below * X – COS X lim O infinity pi O 1 о

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: