1. (a) Give a clear and concise delinition of L.
(b) Evaluate the following limits:
2r 1 5
ii:) lim (2-546'-)
2. (a) Cive a clent and concis definition the statement
"J(x) continuous at the point t=
(b) Find value K that the function f(x) is contimous at r = = wheme
(c) Clearly and concisely state the result known as the Extreme Value Theorem for
3. (a) Let A/ i(2- A)-1(2) for /(x) 3x r2 Calculate lim AJ
(h) Evaluate lim
(c) Evaluate lim
4. (a) Give clear and concise definition of the derivative of function. What does the deriva
live of a function al single point vell us aboubits graph al that point?
(h) U=e the definition of derivative to find 1'(2) for fix) = 3x 7
(c) Find the equation of the tangent line the graph of the function ((x) 3x - 2" at
point (2,2) What the area the triangle formed b this tangent line and the positive
6. Leu y(x) be delined implicitly by he quation any sty. Find y in torms of and
(a) What the domain of the function /(x) ?
(b) Use logarithunic differentiation to find l'(x)
(c) For what values of P'x) =07
0 Use L'Hopital's rule find the following, limits
12. Sketch the graph of the curve y Besure to find the intervals of increase,
decrease and constant concavity and all local extremes and inflection points
1. (a) Give elear and concial definition of
(b) What are the following limits?
lim T-1 x-1
ie) & x²) vi) lim 2x2-1
2. (a) Civonelear and poncine definition ofthe
/(x) continuous al the point z=c",
Give clear and cono definition ofte statement
/(x) contannons on the closod interval Ja,
(c) compound /(x) j(x)
Let the function be defined by
i. Calculate Lin /(x) and [(x).
ii. For what value of Kis the function /(x) s continuous nt:
3. (A) Let A/ h) (1) for 2x Caleulato
(b) Evaluate lime
4. (a) Give cloar and poncise delinition uf derivative uf Junction al a point. What dous
the value c the derivative of function at single point tell us about its tangent line
(b) Use the delinition of derivative wo lind J'(1) for /(x) -1+22+1
(c) Find the equation of the tangent line of the graph of the function /(x) P -2x+
the point 7). Graph this tangent line and find the prea of the triangle formed by this
tangent line and the co ordinate axes.
5. Find the derivativ ves of the following functions. Simplify your answers
b) VI-I 0
7. Let s(2) be delined implicitly by Lie equation t2 12 16.
(a) Findy terms of and y
(b) Findy terms of a andy
9. Usel Hopital's rule or otherwise to find the following limits:
11. Sketch the graph of the curve 8 3x2 2. Be sure to find the intervals increase,
docroase stant coneswity and coordinates local extremes inflection pointa
Alno indicate the number and valuos of any x interecpia (accurato to 2 docimal they
ano not all
1. (a) Give clear and concise definition of lim
(h) Ecaluase the following limits:
in) lim 2 5
lim P-2 m² 81°-2
2. (a) Give clear and concise definition of the statement
"/(x) continnons at the point T=c"
(b) Finda value K so that the function (ix) continuous at x - where
(c) Clearly and concisely state the result known de Lie Intermodiale Value Theorem for
3. (a) Let A/ 13 4) r(3) for /(z) 3x 25 Calculate and
(b) Evaluate lim
4. (a) Give clear and concise definition of the derivative of function What does the deriva
function at. single point cell na about ita graph at that peint?
(b) Use the definition of derivative to ind /(3) for (x) 3a 2
(e) Find the ormation the tangent line of the graph the function j(z) 3x
point (3.0) What sthe area the trianglo formed by thistongent lino and the positivo
5 (a) Find the equation of the tangent line to the curve T³
at its point of
(b) Let y(x) be defined implicitly by the equation 2y y. Find, y al the point (2,2).
7. Lef /(x)= 1)(z
(a) What is the domain the function f(x)
(b) Use dilleventiation to lind l'(x)
(c) For what values of in the domain of ((x)=1
state result known asthe Moan Value Theorem for differentinble