can you do calc 1
aziz jaber
ws11-2.pdf
MAT136 Calculus I Worksheet #1 Name
Full credit will be given only where all reasoning and work is provided. Where appropriate, please enclose your final answers in boxes.
1. Exercise 2.1.4 on page 13 of the book.
2. Exercise 2.2.1 on page 13-14 of the book. Remember that speed is the absolute value of velocity and velocity is given by the slope of the tangent line at each time value.
3. For each function below 1) Graph the function, 2) sketch the tangent line to that function (using a dashed line) at the given point and THEN 3) use the dashed line to find the derivative of the function at the given point. Do not use any shortcuts you may know for the derivative. (a) f(x) = x2 + 3 at x = 0 (b) g(x) = cos x at x = 0
(c) h(x) = ax where a ∈ R at any x (d) f(x) = c where c ∈ R at any x
4. Given the graph of f (assume f continues beyond the box) find the following: If the limit does not exist also state why it does not exist.
(a) lim x→1−
f =
(b) lim x→1+
f =
(c) lim x→1
f =
(d) lim x→2
f(x) =
(e) lim x→3
f =
(f) f(3) =
(g) lim x→4
f =
(h) lim x→−1−
f =
(i) lim x→−1+
f(x) =
(j) lim x→−1
f =
(k) lim x→∞
f(x) =
(l) lim x→−∞
f =
(m) lim x→−4
f =
(n) lim x→−3
f =
(o) f(−3) = (p) lim
x→0 f =
f (x) = 3x f !(x) = 3 x y = 3x d
dx 3x = 3
x !" 4 x !" 0 x
x !" |x| 0 0
x !" #
x 0 0 [0, $)
x(t) t v(t) = x!(t) a(t) = v!(t) = x!!(t)
s(t) = |v(t)|
3 m s
0 m s
%3 m s
3 m s
f !(0) f (x) = x2
cos!(0) sin!( !
2 )
d
dx ax
d
dx c
sign!(0)
f !(0) f (x) = #
x
f !(0) f (x) = 3 #
x
f f !
f &
& &
& •
•• •
f !
& &
&
&
& &
x !" 2 x !" %3x x !" |x| x !" 'x( x !" ln(x) x !" x % 'x(
f !(2) f (x) = x2 2 y 2 2 2 y
y 2
s(y) := f (y) % f (2)
y % 2 = y2 % 22 y % 2 =
(y % 2)(y + 2) y % 2
5. Sketch a graph of a function that satisfies the conditions: lim x→3+
g(x) = 4, lim x→3−
g(x) = 2, lim x→−2
g(x) = 2,
g(3) = 3, and g(−2) = 1.
2
6. Evaluate the limit. (Do not use L’Hopitals rule if you know what that is- save that secret for later!)
(a) lim x→2
x2 + x− 2 x + 2
(b) lim x→2
x2 + x− 6 x− 2
(c) lim t→−3
t2 − 9 t2 + 136
(d) lim h→0
(4 + h)2 − 16 h
(e) lim x→2
√ x3 + 1
(f) lim x→−2
√ x3 + 1
(g) lim x→−1
x2 + 2x + 1
x4 − 1
(h) lim x→0+
ln x
(i) lim x→0
ln x
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