stud
bud
Sign up
Log in
Home
Library
Explore
SAT
More
Quiz! for Calculus I Flashcards | StudBud
Explore
/
Quiz! for Calculus I
Quiz! for Calculus I
9 terms
·
StudBud Administration
·
14 plays
Let this quiz inspire your own quiz for formative assessment.
Flashcards
9 cards
F
Practice quiz
P
Host live
L
Questions
9
Answers
1
Continuous functions are all differentiable.
False
True
2
When you get f'\left(a\right)=0, then x=a could be...
A constant function.
\infty
Either the absolute maximum or the absolute minimum.
Neither a maximum nor a minimum.
3
All derivatives of trigonometric functions came, ultimately, from \lim_{x\to0}\frac{\sin x}{x}=1.
False
True
4
Given a diff-bl fun f(x), the st. line thru \left(a,f\left(a\right)\right) and \left(b,f\left(b\right)\right) is called
a cotangent
a cosecant
a secant
a tangent
5
u=\sec\left(x\right)\tan\left(y\right)⇒\frac{du}{dy}=\sec\left(x\right)\sec^2\left(y\right) What's wrong?
You did not apply product rule.
The differentiation w.r.t. y was wrong
The derivative notation is incorrect.
u should always be written as u\left(x,y\right)
6
We are reviewing the more important part of Calculus for modelling... which is...
Differentiation, because we need to differentiate many times.
Integration, just so to fry your brains as an experiment.
Fundamental Theorem of Calculus, coz it is the central idea of Calculus.
Differentiation, because it models change.
7
What is a good definition of differentiability of f\left(x\right) at x=a?
exist m & E(x) s.t. f(x)-f(a)=m(x-a)+E(x), E(x)->0 as x -> a
m=\lim_{t\to0}\frac{f\left(a+t\right)-f\left(a\right)}{t} exist
f'\left(a\right) exist
m=\lim_{x\to a}\frac{f\left(x\right)-f\left(a\right)}{x-a} exist
8
We still need to remember basic facts, though... The derivative of sec(x) is...
\tan\left(x\right)
-\sec\left(x\right)\tan\left(x\right)
\sec\left(x\right)\tan\left(x\right)
\sec^2\left(x\right)
9
Which of the following function is differentiable for all x\inℝ?
g\left(x\right)=\int_a^x\frac{\sin t}{t}dt
f\left(x\right)=\left|x\right|
h\left(x\right)=\frac{\sin x}{x} if x\ne0, and h\left(0\right)=1
\sin\left(\cos\left(\sin\left(\cos\left(x\right)\right)\right)\right)
