#Q1: Write a function to convert cm to inches (2.54 cm = 1 inch). cm2inch:=x->x/2.54; NiM+SShjbTJpbmNoRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiY5JCIiIiQiJGEjISIjISIiRiVGJUYl cm2inch(5.08); NiMkIisrKysrPyEiKg== #Q2: Write a function that takes as input a single integer n and outputsthe last digit of 2^n. Call the function on n=10,11,12,13,14. Hint: check out the function irem.
lastdig:=x->irem(2^x,10); NiM+SShsYXN0ZGlnRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUklaXJlbUdJKnByb3RlY3RlZEdGLjYkKSIiIzkkIiM1RiVGJUYl lastdig(10);lastdig(11);lastdig(12);lastdig(13);lastdig(14); NiMiIiU= NiMiIik= NiMiIic= NiMiIiM= NiMiIiU= #Q3: Write a function that takes a single real number x as input and outputs the value of 3x^2+exp(x)+sin(x).
q3func:= x->3*x^2+exp(x)+sin(x); NiM+SSdxM2Z1bmNHNiJmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsKCokOSQiIiMiIiQtSSRleHBHRiU2I0YuIiIiLUkkc2luR0YlRjNGNEYlRiVGJQ== #Q4: Plot the above function over -Pi <= x <= Pi and label the axes. Give a title to the plot (the title does not have to be very informative).
plot(q3func(x),x=-Pi..Pi,labels=["dependent variable","function value"],title="Plot for Q4"); 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 #Q5: Write a function that takes a single input (an integer n) returns the integer 1 if n is prime and 0 otherwise. You will only test this function with integers and so no input type specification/checking is needed. Call the function with inputs 23, 871, 873 and 9876543.
q5func:=n->piecewise(isprime(n),1,not isprime(n),0); NiM+SSdxNWZ1bmNHNiJmKjYjSSJuR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSpwaWVjZXdpc2VHSSpwcm90ZWN0ZWRHRi42Ji1JKGlzcHJpbWVHRiU2IzkkIiIiNEYwIiIhRiVGJUYl q5func(23);q5func(871); q5func(873); q5func(9876543); NiMiIiI= NiMiIiE= NiMiIiE= NiMiIiE= #Q6: In a single plot, draw 2 line segments, one from (1,1) to (2,2) and the other from (2,2) to (3,1). Label only the x axis (as "x") and give a title to the plot.
q6func:=piecewise(1<=x and x<=2,x,2<x and x<=3,4-x); NiM+SSdxNmZ1bmNHNiItSSpQSUVDRVdJU0VHRiU2JDckSSJ4R0YlMzEsJiIiIkYuRiohIiIiIiExLCZGKkYuISIjRi5GMDckLCYiIiVGLkYqRi8zMiwkRipGL0YzMSwmRipGLiEiJEYuRjA= plot(q6func(x),x=1..3,labels=["x",""],title="plot for Q6"); 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 #Q7: In the same plot, draw a semicircle with centre (1,0), radius 1 and containing all non-negative y values. Also close the semicircle by drawing the diameter that lies on the x axis. Use an appropriate color so that the line can be seen on the screen.
plot({sqrt(1-(1-x)^2),0},x=0..2,thickness=3); 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