Question

L is the (a) ____ of f(x) as x approaches a if for any possible precision, P>0 (which is (b) ______), then we can find a tolerance, t>0 (which is (c) ______ that forces f(x) to output values less than (d) ______ units from (e) ______ when the input x is less than (f) ______ units from (g) ______.

a) Limit, positive, tolerance, P, t, L, a
b) Derivative, negative, precision, P, t, L, a
c) Integral, zero, sensitivity, S, t, L, x
d) Slope, non-zero, margin, M, t, L, a

Answer 1

The term 'L' in the mathematical context provided refers to the limit of a function as x approaches a certain value, which is the correct completion of the sentence relating to limits in calculus.

Step-by-step explanation:

The term 'L' in the context of the question refers to the limit of a function as x approaches a certain value. To address the gaps in the question:

1. L is the limit of f(x) as x approaches a,
2. Any possible precision, P, must be positive,
3. The term 't>0' refers to a tolerance,
4. This tolerance is bound by the condition that f(x)'s output values are less than P units from L when x is within the tolerance t from a.

The correct completion of the sentence would be: L is the limit of f(x) as x approaches a if for any possible precision, P>0 (which is positive), then we can find a tolerance, t>0 (which is tolerance) that forces f(x) to output values less than P units from L when the input x is less than t units from a.