- #1
AllanW
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Homework Statement
if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places
Homework Equations
(f(x+h)-f(x))/h
The Attempt at a Solution
On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91
No, the limit at the top is not the same as sin(2).AllanW said:Homework Statement
if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places
Homework Equations
(f(x+h)-f(x))/h
The Attempt at a Solution
On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91
AllanW said:Homework Statement
if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places
Homework Equations
(f(x+h)-f(x))/h
The Attempt at a Solution
On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91
In this equation, "lim x→2" means that we are looking at the behavior of the function as x approaches the value of 2. It is known as the limit of the function.
While "sin(2)" is evaluating the sine function at the specific value of 2, "lim x→2 sin(x)" is looking at the limit of the function as x approaches 2. In other words, "lim x→2 sin(x)" is analyzing the behavior of the function near the value of 2, rather than just evaluating it at that point.
Yes, we can solve "lim x→2 sin(x)" by using various methods such as L'Hopital's rule, trigonometric identities, or graphing the function. The exact method will depend on the complexity of the function.
The limit of a function, such as "lim x→2 sin(x)", helps us understand the behavior of the function at a specific point. In this case, it tells us how the sine function approaches the value of 2, which can be useful in understanding the behavior of more complex functions that involve the sine function.
No, the value of "lim x→2 sin(x)" is determined by the function itself and cannot be changed. However, we can change the value of x that we are approaching, which will in turn change the value of the limit. For example, "lim x→3 sin(x)" will have a different value than "lim x→2 sin(x)".