MAT135 Calculus 1 Final Exam | Questions and Answer Key | 2026 Update |
100% Correct - University of Toronto Already Graded A+.
sin^2x+cos^2x - (ANSWER)=1
equation of a tangent line - (ANSWER)y-y0 = m(x-x0) at point (x0, y0) and slope m
Limit of a Function - (ANSWER)Value a function approaches as x approaches a point.
Sum Limit Law
lim (f(x) + g(x)) = - (ANSWER)lim f(x) + lim g(x)
Difference Limit Law
lim ( f(x) - g(x) ) = - (ANSWER)lim f(x) - lim g(x)
Constant Multiple Limit Law
lim cf(x) = - (ANSWER)c * lim f(x)
Product Limit Law
lim (f(x) * g(x)) = - (ANSWER)lim f(x) * lim g(x)
Quotient Limit Law
lim ( f(x)/ g(x) ) = - (ANSWER)lim f(x) / lim g(x) , as long as lim g(x) is not 0.
, MAT135 Calculus 1 Final Exam | Questions and Answer Key | 2026 Update |
100% Correct - University of Toronto Already Graded A+.
Power Limit Law
lim( f(x)^n ) = - (ANSWER)(lim f(x)) ^n
Polynomial Limits
lim f(x) =
x->a - (ANSWER)lim f(a)
Rational Limits
lim = f(x)/g(x) =
x->a - (ANSWER)f(a)/g(a)
lim sinx/x =
x ->0 - (ANSWER)1
lim (cosx -1)/x =
x-> 0 - (ANSWER)0
end behavior of a rational function (degree n < degree d) - (ANSWER)if n < d, lim = 0 and HA at y=0
end behavior of a rational function (degree n > degree d) - (ANSWER)if n > d, lim = infin. or negative infin.
and there is no HA
end behavior of a rational function (degree n = degree d) - (ANSWER)if n=d, limit is a/b and HA at y= a/b,
where a and b are leading terms of the num. and denom. respectively
100% Correct - University of Toronto Already Graded A+.
sin^2x+cos^2x - (ANSWER)=1
equation of a tangent line - (ANSWER)y-y0 = m(x-x0) at point (x0, y0) and slope m
Limit of a Function - (ANSWER)Value a function approaches as x approaches a point.
Sum Limit Law
lim (f(x) + g(x)) = - (ANSWER)lim f(x) + lim g(x)
Difference Limit Law
lim ( f(x) - g(x) ) = - (ANSWER)lim f(x) - lim g(x)
Constant Multiple Limit Law
lim cf(x) = - (ANSWER)c * lim f(x)
Product Limit Law
lim (f(x) * g(x)) = - (ANSWER)lim f(x) * lim g(x)
Quotient Limit Law
lim ( f(x)/ g(x) ) = - (ANSWER)lim f(x) / lim g(x) , as long as lim g(x) is not 0.
, MAT135 Calculus 1 Final Exam | Questions and Answer Key | 2026 Update |
100% Correct - University of Toronto Already Graded A+.
Power Limit Law
lim( f(x)^n ) = - (ANSWER)(lim f(x)) ^n
Polynomial Limits
lim f(x) =
x->a - (ANSWER)lim f(a)
Rational Limits
lim = f(x)/g(x) =
x->a - (ANSWER)f(a)/g(a)
lim sinx/x =
x ->0 - (ANSWER)1
lim (cosx -1)/x =
x-> 0 - (ANSWER)0
end behavior of a rational function (degree n < degree d) - (ANSWER)if n < d, lim = 0 and HA at y=0
end behavior of a rational function (degree n > degree d) - (ANSWER)if n > d, lim = infin. or negative infin.
and there is no HA
end behavior of a rational function (degree n = degree d) - (ANSWER)if n=d, limit is a/b and HA at y= a/b,
where a and b are leading terms of the num. and denom. respectively
