Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Limit Calculation and Function Continuity, Exams of Calculus

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

Pre 2010

Uploaded on 08/03/2009

koofers-user-scg
koofers-user-scg 🇺🇸

10 documents

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
lim
x3f(x) =3 lim
x3g(x) = 10
lim
x3
2f(x)
g(x) f(x)
F x
(
)
=2x
x2+ 5 x+ 6
g x
(
)
= sin1x21
(
)
lim
x9+ln (x9)
y=2x27x
f' (a)
f(t) = 3t+ 3
t+ 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 .
PAGE 1
Name: __________________ Class: Date: _____________
pf3

Partial preview of the text

Download Limit Calculation and Function Continuity and more Exams Calculus in PDF only on Docsity!

lim x  3 f(x) =  3 lim x  3 g(x) = 10

x^ lim  3 g(x)^2 f(x)  f(x)

F ( x ) = 2 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

f ( x ) = x^3  16 x + 7

lim h  0

cos (3  + h ) + 1 h

f ( x ) =

1  x x <  1 x  1  x < 3

{ ( x  3)^2 x  3

lim x a f ( x )

f ( 3 ) = 1

lim

x  3 2 f^ (^ x )^  g^ (^ x )^ =^3 g^ (^3 )

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: _____________