Answer:
Amount spent after sales tax = $112.58
Step-by-step explanation:
Given that:
Cost of jacket = $49.00
Cost of new Vans = $55.00
Total spent = 49.00 + 55.00 = $104.00
Sales tax = 8.25%
Amount of sales tax =
Amount of sales tax = $8.58
Total after sales tax = 104.00 + 8.58 = $112.58
Hence,
Amount spent after sales tax = $112.58
1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:
Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.
2. f(x) is continuous at x = -1, so the limit can be computed directly again:
3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So
4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.
5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case
When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.
6. It should be rather clear from the plot that
because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.
For 7-8, divide through each term by the largest power of x in the expression:
7. Divide through by x². Every remaining rational term will converge to 0.
8. Divide through by x² again:
9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:
10. Factorize the numerator and simplify:
where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is
Answer:
t= 11
Step-by-step explanation:
Gradient of line that contains points (3, 7) & (5, 11)
= 2
The product of the gradients of two perpendicular lines is -1.
Gradient of the line that contains points (t, -2) & (-3, 5)
= -1 ÷2
Cross multiply:
-(t +3)= -7(2)
Dividing by -1 on both sides:
t +3= 7(2)
t +3= 14
t= 14 -3
t= 11