Podcast
Questions and Answers
What is the value of $\lim_{z\to 2}\frac{z^2-5z+6}{z^2-4}$?
What is the value of $\lim_{z\to 2}\frac{z^2-5z+6}{z^2-4}$?
If $5^{2x+7}=125$, what is the value of x?
If $5^{2x+7}=125$, what is the value of x?
Which of the following represents the associative property of sets?
Which of the following represents the associative property of sets?
What is the slope of the line with an inclination of $\frac{\pi}{4}$?
What is the slope of the line with an inclination of $\frac{\pi}{4}$?
Signup and view all the answers
Signup and view all the answers
Flashcards
Limit of a function
Limit of a function
The value that a function approaches as the input approaches a specific point.
Exponent equation
Exponent equation
An equation where the variable is in the exponent, such as $5^{2x+7} = 125$.
Associativity property
Associativity property
A property stating that the way numbers are grouped does not change their sum or product, like $(A∪B)∪C = A∪(B∪C)$.
Slope of a line
Slope of a line
Signup and view all the flashcards
Set-Builder notation
Set-Builder notation
Signup and view all the flashcards
Study Notes
Q.1 Select and Write the Correct Answer
- Evaluate lim (x²-5x+6)/(x²-4): ½
- If 5^(2x+7)=125, then x =?: 2
- Associativity property belongs to: (AuB)u C = Au(BuC)
Q.2 Answer the Following (Attempt any THREE)
- Slope of a line with inclination π/4: 1
- Evaluate lim (1+2)/(1-x): 3
- If f(m)=m²-3m+1, find f(-3) and f(x+1): f(-3)=19; f(x+1) = x²+x-1
- Given U, A, B, and C sets, find (A∪B)′: (1,2,3,4,6,8).
Q.3 Attempt any Five
- Domain of log(x-5): x > 5
- Equation of line with slope and passing through (-1,2): y = 2x + 4
- Set-Builder form of sets A and B: A = {0, 1, 2, 3}; B = {1, 2, 3, 4, 5/2, 10/5, 26}
- Arrow diagram for relation x<y given A={1,2,3,4,5} and B={1,4,5}: Draw arrows from each element in A to each element in B which is greater than it.
- Center and diameter of circle x²+y²-6x-8y-24=0: Center (3, 4); Diameter 10
- If A={a,b,c} and B={x,y}, find A×B, A×A, B×A: A×B = {(a,x), (a,y), (b,x), (b,y), (c,x), (c,y)}; A×A = {(a,a), (a,b), (a,c), (b,a), (b,b), (b,c), (c,a), (c,b), (c,c)}; B×A = {(x,a), (x,b), (x,c), (y,a), (y,b), (y,c)}
Q.4 Attempt any THREE
- If points A(h,0), B(0,k), C(a,b) lie on a line, show that (a/h) = (b/k)=1: Show that (a/h) = (b/k) = 1 implies points A(h,0), B(0,k), and C(a,b) are collinear.
- Domain and range of f(x)=√(9-x²): Domain: -3 ≤ x ≤ 3; Range: 0 ≤ f(x) ≤ 3
- Acute angle between lines y-√3x+1=0 and √3y-x+7=0: 15°
- Evaluate limits sin80/(tan40) and log81/log9: √3
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers various topics in mathematics, focusing on limits, properties of functions, and relationships between sets. Students will solve problems related to slope, function evaluation, and set operations. Perfect for reinforcing key concepts from the mathematics curriculum.
