MTH 251 Midterm 1
Continuity tick list - ANS-1) f is described at a 2) limx->a f(x) exists 3) limx->af(x)=f(a)
Definiton of a limit - ANS-Suppose a function f is described for all x near a point a, however
probable now not all a (doesn't need to be defined at a, but must be round point a). If f(x) is
arbitrarily close to a positive range L wheneverx is satisfactorily close to however equal to a
than L is a restriction of f as x techniques a
if the characteristic f is continuous at x=a, then f should also be differentiable at x=a -
ANS-False
Intermediate price theorem (IVT) - ANS-If f is non-stop on interval [a,b] and L is between f(a)
and f(b) then there's a price(s) c in (a,b) such that f(c)=L
is it differentiable? - ANS-continuous does not imply differentiable (absolute fee), not
non-stop=not differentiable
lim x->a^- - ANS-tactics from left
lim x->a^+ - ANS-strategies from right
limits at infinity of rational radical features - ANS-even energy signal of infinity does not
remember extraordinary electricity signal does be counted
mathematical definition of a limit - ANS-limx->a f(x)=L
no longer removable discontinuties - ANS-bounce, limitless (asymptote)
detachable discontinuities - ANS-a hole, can be factored out of the equation
Removable discontinuity: - ANS-A detachable discontinuity is a discontinuity that disappears
if f(a) s redefined to that f(a)=lim as x->af(x)
vertical asymptote - ANS-A vertical asymptote is a vertical line x
=a, which the graph of a characteristic tactics as x techniques a.
Continuity tick list - ANS-1) f is described at a 2) limx->a f(x) exists 3) limx->af(x)=f(a)
Definiton of a limit - ANS-Suppose a function f is described for all x near a point a, however
probable now not all a (doesn't need to be defined at a, but must be round point a). If f(x) is
arbitrarily close to a positive range L wheneverx is satisfactorily close to however equal to a
than L is a restriction of f as x techniques a
if the characteristic f is continuous at x=a, then f should also be differentiable at x=a -
ANS-False
Intermediate price theorem (IVT) - ANS-If f is non-stop on interval [a,b] and L is between f(a)
and f(b) then there's a price(s) c in (a,b) such that f(c)=L
is it differentiable? - ANS-continuous does not imply differentiable (absolute fee), not
non-stop=not differentiable
lim x->a^- - ANS-tactics from left
lim x->a^+ - ANS-strategies from right
limits at infinity of rational radical features - ANS-even energy signal of infinity does not
remember extraordinary electricity signal does be counted
mathematical definition of a limit - ANS-limx->a f(x)=L
no longer removable discontinuties - ANS-bounce, limitless (asymptote)
detachable discontinuities - ANS-a hole, can be factored out of the equation
Removable discontinuity: - ANS-A detachable discontinuity is a discontinuity that disappears
if f(a) s redefined to that f(a)=lim as x->af(x)
vertical asymptote - ANS-A vertical asymptote is a vertical line x
=a, which the graph of a characteristic tactics as x techniques a.
