Looks good to me.AlexandraMarie112 said:Homework Statement
f(x)= (sincx/x) ; x<0
1+(c)(tan2x/x) ; x≥0
Homework Equations
The Attempt at a Solution
Lim as x tends to 0+[/B] = 1+c⋅2⋅(sin2x/2x)⋅(1/cos2x) =1+c⋅2⋅1⋅1= 1+2c
Lim as x tends to 0 - = (sincx/x)=(c/1)⋅(sinx/x)=c⋅1=c
Equating both: 1+2c=c
c=-1
∴For the function to be continuous at x=0, c=-1
Is my answer correct?
Continuous functions are those that have no abrupt jumps or holes in their graph. This means that the function can be drawn without having to lift your pencil from the paper.
Finding the value of c that makes a function continuous is important because it ensures that the function is well-defined and can be evaluated at all points within its domain. This allows for a better understanding and analysis of the function.
To find the value of c, you need to set the two pieces of the function equal to each other and solve for c. This will give you the point where the two pieces of the function will meet and make the function continuous.
Yes, it is possible for there to be multiple values of c that make a function continuous. This usually occurs when there are multiple pieces to the function and the value of c can vary depending on which pieces are being joined.
No, it is not always possible to find the value of c that makes a function continuous. This usually occurs when the two pieces of the function have different behaviors at the point where they are supposed to meet, making it impossible to find a single value of c that will make the function continuous.