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A set of mathematical problems focused on evaluating limits, finding equations of tangent lines, and determining the continuity of functions. The problems involve finding limits of functions, equations of tangent lines to parabolas, and values of functions at specific points. Students are also asked to find derivatives using the definition of derivative and determine the existence of limits for given functions.
Typology: Exams
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lim x 3 f(x) = 3 lim x 3 g(x) = 10
x^ lim 3 g(x)^2 f(x) f(x)
x^2 + 5 x + 6
g (^) ( x ) = sin ^1 ( x^2 1 )
lim x 9 +
ln ( x 9)
y = 2 x^2 7 x
f ' ( a )
f ( t ) = (^3) t^ t + 3+ 3
1 Given that,
Evaluate the limit:
2 Write an equation that expresses the fact that a function f is continuous at the number 4.
3 State the domain.
4 Over what interval(s) is the following function continuous?
5 Find the limit.
6 Find an equation of the tangent line to the parabola at the point ( 5, 15 ).
7 Find.
Name: __________________ Class: Date: _____________
lim h 0
(1 + h )^3 1 h
lim x 5
5 x^^ 3125 x 5
lim h 0
cos (3 + h ) + 1 h
f ( x ) =
1 x x < 1 x 1 x < 3
lim x a f ( x )
lim
8 The limit represents the derivative of some function f at some number a.
.
State f and a.
9 The limit represents the derivative of some function f(x) at some number a.
State f(x).
.
10 Find the derivative of the function using the definition of derivative.
11 The limit represents the derivative of some function f(x) at some number a.
State f(x) and a.
.
12 Consider the following function,
and determine the values of a for which exists.
13 If f and g are continuous functions with and
, find
Name: __________________ Class: Date: _____________