For what intervals is f(x) = tan((pix)/4) continuous? Calculus Limits Definition of Continuity at a Point 1 Answer sente Nov 13, 2015 tan((pix)/4) is continuous on intervals of the form (2 + 4k, 2 + 4(k+1)), k in ZZ Explanation: tan(x) is continuous on (pi/2 + kpi, pi/2 + (k+1)pi), k in ZZ So tan((pix)/4) is continuous where (pix)/4 lies within such an interval. That is, where pi/2 + kpi < (pix)/4 < pi/2 + (k+1)pi Multiplying through by 4/pi gives us 2 + 4k < x < 2 + 4(k+1) Thus tan((pix)/4) is continuous on (2 + 4k, 2 + 4(k+1)), k in ZZ Answer link Related questions What are the three conditions for continuity at a point? What is continuity at a point? What is the definition of continuity at a point? What does continuous at a point mean? What makes a function continuous at a point? How do you find the points of continuity and the points of discontinuity for a function? What does continuity mean? How do you use continuity to evaluate the limit arctan(x^2-4)/(3x^2-6x)? How do you find the points of continuity of a function? How do you find the continuity of a function on a closed interval? See all questions in Definition of Continuity at a Point Impact of this question 5912 views around the world You can reuse this answer Creative Commons License