1.1 Übungen
Aus Online Mathematik Brückenkurs 2
| Theory |
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Exercise 1.1:1
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The graph for \displaystyle f(x) is shown in the figure.
(Each square in the grid of the figure has width and height 1.) | 1.1 - Figur - Grafen till f(x) i övning 1.1:1 |
Answer
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Solution a
Solution b
Solution c
Exercise 1.1:2
Determine the derivative \displaystyle f^{\,\prime}(x) when
| a) | \displaystyle f(x) = x^2 -3x +1 | b) | \displaystyle f(x)=\cos x -\sin x | c) | \displaystyle f(x)= e^x-\ln x |
| d) | \displaystyle f(x)=\sqrt{x} | e) | \displaystyle f(x) = (x^2-1)^2 | f) | \displaystyle f(x)= \cos (x+\pi/3) |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 1.1:3
A small ball, that is released from a height of \displaystyle h=10m above the ground at time \displaystyle t=0, is at a height \displaystyle h(t)=10-\displaystyle\frac{9{,}82}{2}\,t^2 at time \displaystyle t (measured in seconds) What is the speed of the ball when it hits the grounds?
Answer
Solution
Exercise 1.1:4
Determine the equation for the tangent and normal to the curve \displaystyle y=x^2 at the point \displaystyle (1,1).
Answer
Solution
Exercise 1.1:5
Determine all the points on the curve \displaystyle y=-x^2 which have a tangent that goes through the point \displaystyle (1,1).
Answer
Solution
