To evaluate a limit as x approaches a value, first check if the denominator equals zero at that point; if not, the function is continuous and the limit can be found by direct substitution. For the limit as x approaches 1 of (4x³ + x - 7)/(2 - x²), substituting x = 1 gives (4(1)³ + 1 - 7)/(2 - 1²) = (4 + 1 - 7)/1 = -2/1 = -2.
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Can You Solve This Limit?Added:
Can you solve this limit as X approaches one of four X cubed plus X minus seven divided by two minus X squared?
First, check whether the denominator is zero when X equal to one.
Substitute one for X.
Two minus one squared equal to one.
Since the denominator is not zero, the function is continuous at X equal to one, so we can evaluate the limit by direct substitution.
Again, we will substitute one for X.
Four times one cubed plus one minus seven divided by two minus one squared.
Simplify, we have negative two over one equal to negative two.
The limit is negative two.
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