Finding the Value of b to Make f Continuous at x=0

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The discussion focuses on determining the value of b that ensures the function f(x) is continuous at x=0, defined as f(x) = [(e^x) - 1] / x for x ≠ 0 and f(0) = b. To achieve continuity, the limit of f(x) as x approaches 0 must equal b. The limit is calculated as the expression [(e^x) - 1] / x, which simplifies to 1 when evaluated at x=0, leading to the conclusion that b must equal 1 for f to be continuous at that point.

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f(x) = { [(e^x) - 1] / x ; if x not equal 0
... .{ b ......; if x = 0

What value of b makes f continuous at x = 0?

so.. the left side and right side must be equal in order to make
f continuous at x = 0

[(e^x) - 1] / x = b
[(e^x) - 1] = (b)(x)
e^x = (b)(x) + 1
.
.
.
dont know how to proceed..

should i introduce ln?
 
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