Answer with Step-by-step explanation:
We are given that
We have to prove that why the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form and prove that the limit equals to 0.
Because and
We know that cos 0=1 and sin 0=0
Substitute the values then we get
We know that is indeterminate form
Hence, the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form.
L'hospital rule:Apply this rule and differentiate numerator and denominator separately when after applying we get indeterminate form
Now,using L' hospital rule
because
Now, we get
Hence,
7and 5/8
5+2 is 7
3/8+2/8 is 5/8
7+5/8 is
7 and 5/8
Answer:
3 1/8
Step-by-step explanation:
note that the zeroes should be x = 1 and x = - 2 not x = - 1 and x = 2
the factors are then ( x - 1 ) and (x + 2)
and x³ - 4x² - 7x + 10 = (x - 1 )(x + 2) = x² + x - 2
thus x² + x - 2 is a factor
dividing x³ - 4x² - 7x + 10 by x² + x - 2 gives x - 5
the third zero is x = 5
check : (5)³ -4(5)² - 7(5) + 10 = 125 - 100 - 35 + 10 = 0