Mat 101

Task 1

Find the limit values:

Task 2

Find all vertical and horizontal asymptotes to

Task 3

Find the sums:

( b is to infinity)

Task 4

The concentration of an algae in the fjord varies periodically with a period of 12 months. Call this concentration M(t) where t is time in months from 1 January of a year. The biggest the value of M(t) is M(7) = 500 and the smallest value is M(1) = 100.

a) Assume that M(t) can be expressed in the form

Determine C0, C, T and t0 from the information given above.

b) When in the year is M(t) = 400?

c) A biologist surveys two algae, A and B, which are found in the fjord at the same time. They grow differently:

What is the maximum value for A(t) + B(t)? plots with a suitable tool and reads the graph.

Task 5

a) Find all solutions that fulfills 0 = t = 2p:

b) Write 5 cos (3t) - 12 sin (3t) in the form C cos (? (t - t0)).

Task 6

You boil one egg. When you take the egg out of the boiling water, the temperature inside the egg is 90?C. The temperature in the room is 20?C. 77 seconds after the egg is taken out of the water, the temperature in the egg is 80?C. Let E(t) denote the temperature inside the egg, where t is the time in seconds from when the egg is taken out of the boiling water. We assume that the difference between E(t) and the room temperature decreases exponentially, which means

Determine c and a from the information given above. How long does it take from the time the egg is taken out of the boiling water until the temperature in the egg is 40?C?

Task 1

Find the limit values:

Task 2

Find all vertical and horizontal asymptotes to

Task 3

Find the sums:

( b is to infinity)

Task 4

The concentration of an algae in the fjord varies periodically with a period of 12 months. Call this concentration M(t) where t is time in months from 1 January of a year. The biggest the value of M(t) is M(7) = 500 and the smallest value is M(1) = 100.

a) Assume that M(t) can be expressed in the form

Determine C0, C, T and t0 from the information given above.

b) When in the year is M(t) = 400?

c) A biologist surveys two algae, A and B, which are found in the fjord at the same time. They grow differently:

What is the maximum value for A(t) + B(t)? plots with a suitable tool and reads the graph.

Task 5

a) Find all solutions that fulfills 0 = t = 2p:

b) Write 5 cos (3t) - 12 sin (3t) in the form C cos (? (t - t0)).

Task 6

You boil one egg. When you take the egg out of the boiling water, the temperature inside the egg is 90?C. The temperature in the room is 20?C. 77 seconds after the egg is taken out of the water, the temperature in the egg is 80?C. Let E(t) denote the temperature inside the egg, where t is the time in seconds from when the egg is taken out of the boiling water. We assume that the difference between E(t) and the room temperature decreases exponentially, which means

Determine c and a from the information given above. How long does it take from the time the egg is taken out of the boiling water until the temperature in the egg is 40?C?

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