Squeeze theorem - Samenvattingen, Aantekeningen en Examens
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Calculus 1 UPDATED Exam Questions and CORRECT Answers
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Squeeze Theorem 
f is continuous at x=c if... 
Intermediate Value TheoremIf f is continuous on [a,b] and k is a number between f(a) 
and f(b), then there exists at least one number c such that f(c)=k 
Global Definition of a Derivative 
Alternative Definition of a Derivativef '(x) is the limit of the following difference 
quotient as x approaches c
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AP Calculus BC All of the theorems and rules you will need to know for the Calculus BC test.
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AP Calculus BC All of the theorems and rules you will need to know for the Calculus BC test. 
 
If h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim x→c ƒ(x) exists and equals L. - Answer>>Squeeze Theorem 
 
A function ƒ is continuous at c if: 
a. ƒ(c) is defined 
b. lim x→c ƒ(x) exists 
c. lim x→c ƒ(x) = ƒ(c) - Answer>>Continuity
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MATH 221 Midterm 1 Exam Questions with 100% Correct Answers
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Secant Line Correct Answer The line connecting any two points on a curve. 
 
Tangent Line Correct Answer The line that best approximates a function near a point A. It's the limit of secant lines connecting points A & B as B approaches A. 
 
Squeeze Theorem Correct Answer If f(x)≤g(x)≤h(x) and if the top and bottom functions both have the same limits, we can conclude that the middle function must have the same limit. 
 
Continuity Correct Answer A function, f, is continuous at x=a if the lim...
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MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS
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QUESTION 1 
 
(a)	Determine the following limits (if they exist): 
 
 
(i) 
 
 
 
 
 
 
(3) 
 
 
 
(ii) 
 
x 2 
 
lim 
 
3 x 1 
 
 
2 
 
 
 
 
 
(3) 
 
x 3 x 9 
 
 
(iii) 
 
(iv) 
 
lim 
x 	2x 
lim 1 	x 
 
(3) 
 
(3) 
 
 
 
(v) 
 
x 1 
 
lim 
 
1 x 
2x 
 
 
 
(3) 
 
 
 
 
(vi) 
 
lim sin t tan 2t 
 
 
(3) 
 
t 0	t 
 
(b)	Use the Squeeze Theorem to determine the following limit: 
 
5k 2 cos3k 
lim	2	. 
 
 
 
 
(3) 
 
 ...
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AP Calculus AB
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AP Calculus AB 
 2023 
 
1 - 
0 - 
Squeeze Theorem - 
f is continuous at x=c if... - 
Intermediate Value Theorem - If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k 
Global Definition of a Derivative - 
Alternative Definition of a Derivative - f '(x) is the limit of the following difference quotient as x approaches c 
nx^(n-1) - 
1 - 
cf'(x) - 
f'(x)+g'(x) - 
f'(x)-g'(x) - 
cos(x) - 
-sin(x)...
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MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS 1 [TURN OVER] 2 x 0 3 x 9 x2 x QUESTION 1 (a) Determine the following limits (if they exist): (i) (3) (ii) x 2 lim 3 x 1 2 (3) x 3 x 9 (iii) (iv) lim x 2x lim 1 x (3) (3) (v) x
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MAT1512 EXAM PACK 2023 
LATEST QUESTIONS AND ANSWERS 
1 
[TURN OVER] 
2 
x 0 3 
x 9 
x2 x 
 
QUESTION 1 
(a) Determine the following limits (if they exist): 
(i) 
(3) 
(ii) 
x 2 
lim 
3 x 1 
2 
(3) 
x 3 x 9 
(iii) 
(iv) 
lim 
x 2x 
lim 1 x 
(3) 
(3) 
(v) 
x 1 
lim 
1 x 
2x 
(3) 
(vi) 
lim sin t tan 2t 
(3) 
t 0 t 
(b) Use the Squeeze Theorem to determine the following limit: 
5k 2 cos3k 
lim 2 . 
(3) 
 x ...
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MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS 1 [TURN OVER] 2 x 0 3 x 9 x2 x QUESTION 1 (a) Determine the following limits (if they exist): (i) (3) (ii) x 2 lim 3 x 1 2 (3) x 3 x 9 (iii) (iv) lim x 2x lim 1 x (3) (3) (v) x
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MAT1512 EXAM PACK 2023 
LATEST QUESTIONS AND ANSWERS 
1 
[TURN OVER] 
2 
x 0 3 
x 9 
x2 x 
 
QUESTION 1 
(a) Determine the following limits (if they exist): 
(i) 
(3) 
(ii) 
x 2 
lim 
3 x 1 
2 
(3) 
x 3 x 9 
(iii) 
(iv) 
lim 
x 2x 
lim 1 x 
(3) 
(3) 
(v) 
x 1 
lim 
1 x 
2x 
(3) 
(vi) 
lim sin t tan 2t 
(3) 
t 0 t 
(b) Use the Squeeze Theorem to determine the following limit: 
5k 2 cos3k 
lim 2 . 
(3) 
 x ...
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MAT1512 ExAM PAck 2024 LATEST QUESTIONS AND CORRECT ANSWERS
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a) Determine the following limits (if they exist): 
(i) 
3 1 
6 2 
lim 
2 
 
 
 x 
x 
x 
(3) 
(ii) 
3 9 
lim 
2 
3 
 
 
 x 
x 
x 
(3) 
(iii) 
x 
x x x 
x 2 
4 2 
lim 
2 
 
 
(3) 
(iv) 
xx 
x 
 
 
 1 
1 
lim 
1 
(3) 
(v) 
3 9 
2 
lim 
 0 x 
x 
x 
(3) 
(vi) 
t 
t t 
t 
sin tan 2 
lim 
0 
 
 
(3) 
(b) Use the Squeeze Theorem to determine the following limit: 
. 
10 
5 cos3 
lim 
2 
2 
 
 
 k 
k k 
k 
(3) 
(c) ...
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MAT1512 QUESTIONS AND CORRECT ANSWERS EXAM PACK
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a) Determine the following limits (if they exist): 
(i) 
3 1 
6 2 
lim 
2 
 
 
 x 
x 
x 
(3) 
(ii) 
3 9 
lim 
2 
3 
 
 
 x 
x 
x 
(3) 
(iii) 
x 
x x x 
x 2 
4 2 
lim 
2 
 
 
(3) 
(iv) 
xx 
x 
 
 
 1 
1 
lim 
1 
(3) 
(v) 
3 9 
2 
lim 
 0 x 
x 
x 
(3) 
(vi) 
t 
t t 
t 
sin tan 2 
lim 
0 
 
 
(3) 
(b) Use the Squeeze Theorem to determine the following limit: 
. 
10 
5 cos3 
lim 
2 
2 
 
 
 k 
k k 
k 
(3) 
(c) ...
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NIFE Engines 2023, Top Questions and answers, 100% Accurate. VERIFIED.
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NIFE Engines 2023, Top Questions and 
answers, 100% Accurate. VERIFIED. 
EXPLAIN Bernoulli's Equation, given dynamic pressure, static pressure, and total pressure - - 
Bernoulli's equation Pt=Pdynamic+Pstatic 
Pstatic is potential of fluid molecules at rest. Called pressure in generator 
Pdynamic is kinetic energy of fluid molecules in motion. Called velocity in generator 
Describe Nozzle's effect on velocity and pressure and which subsonic and supersonic airflow shapes - 
-Always increase v...
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