Degree of a term = sum of the powers of variables in that term.
Highest degree term is 8x²y³ with degree 2 + 3 = 5.
Given lim x → 1⁺ (2 + √x - 1)
As x approaches 1 from the right:
√x approaches √1 = 1
So, √x - 1 approaches 1 - 1 = 0
2 + 0 = 2
The limit is 2.
Given f(x) = 6x/(3x - 2)
The denominator cannot be zero:
3x - 2 ≠ 0
3x ≠ 2
x ≠ 2/3
So, the domain of f(x) is all real numbers except x = 2/3.
The answer is R - {2/3}.
The formula for acceleration is a = F/m,
Where
'a' is acceleration,
'F' is net force,
'm' is mass.
The associative property w.r.t addition states that the order in which we add numbers does not change the result.
The correct equation is:
1 + (4 + 3) = (1 + 4) + 3
This equation represents the associative property of addition.
- f tan xdx = ln[cos x] + C.
This is a standard result from integral calculus involving trigonometric functions.
A critical point occurs where the derivative of a function is zero or does not exist.
These points are important for finding local maxima, minima, or points of inflection.
The differential equation xy' = y can be rewritten as y'/y = 1/x.
This equation has a unique solution when x ≠ 0, since dividing by zero is undefined.
The solution exists on the region defined by either x > 0 or x < 0.
To find g(3), substitute t = 3 into the equation:
g(3) = (3)³ + (3)² - 9(3) - 9
= 27 + 9 - 27 - 9
= 0
The quadratic equation whose roots are reciprocal of:
2x2 + 5x + 3 = 0 can be obtained by replacing x by 1/x.
Hence, 2(1/x)2 + 5(1/x) + 3 = 0
=> 3x^2 + 5x + 2 = 0