Calculus Examples

Determine if Continuous f(x)=-3x+7 if x<=3; -2 if x>3
f(x)={-3x+7x3-2x>3
Step 1
Find the limit of -2 as x approaches 3 from the right.
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Step 1.1
Change the two-sided limit into a right sided limit.
limx3+-2
Step 1.2
Evaluate the limit of -2 which is constant as x approaches 3.
-2
-2
Step 2
Evaluate -3x+7 at 3.
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Step 2.1
Replace the variable x with 3 in the expression.
-33+7
Step 2.2
Evaluate.
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Step 2.2.1
Multiply -3 by 3.
-9+7
Step 2.2.2
Add -9 and 7.
-2
-2
-2
Step 3
Since the limit of -2 as x approaches 3 from the right is equal to the function value at x=3, the function is continuous at x=3.
Continuous
Step 4
 [x2  12  π  xdx ]