Limits of Exponential, Logarithmic, and Trigonometric Function GRADE 11 BASIC CALCULUS Exponential and Logarithmic Functions • If π > 0, π ≠ 0, the exponential function with base b is defined by π π = ππ , π ∈ β • Let π > 0, π ≠ 0. If π π¦ = π₯ then π¦ is called the logarithm of π₯ the base b, denoted π = π₯π¨π π π Limits of Exponential Function We will consider the natural exponential function π π₯ = π π₯ , where π is called the Euler number, and has value of 2.718281… Example: Evaluate the lim π π₯→0 π₯ Limits of Logarithmic Function We will consider the natural logarithmic function π π₯ = ln π₯ . Recall that ln π₯ = log π π₯ . Moreover, it is the inverse of the natural exponential function π¦ = ππ₯. Example: Evaluate the lim ln π₯ π₯→1 Limits of Logarithmic Function Evaluate lim log π₯ π₯→1 Limits of Trigonometric Functions Evaluate lim sin π₯ π₯→0 Example π₯ Evaluate lim 3 π₯→1 Example π₯ Evaluate lim 5 π₯→2 Example Evaluate lim log π₯ π₯→4 Example Evaluate lim cos π₯ π₯→0 Example Evaluate lim tan π₯ π₯→0 Example Evaluate lim cos π₯ π₯→π Example Evaluate lim sin π₯ π₯→π • lim cos π₯ π₯→0 • lim cos π₯ π₯→π • limπ cos π₯ π₯→ 2
