ALGEBRA - solved problems
The limit of a function
The limit of a rational function at infinity containing roots (irrational expressions)
 354
Evaluate the limit
 Solution:
 355
Evaluate the limit
 Solution:
The limit of a rational function at a point containing irrational expressions, use of substitution
Use of the method of substitution to avoid the indeterminate form of an expression.
 356
Evaluate the limit
Solution:   Let substitute,   x + 1 =  y6,   then as  x ® 0  then   y ® 1,   therefore
 357
Evaluate the limit
Solution:   Let substitute,   xy12,   then as  x ® 1  then   y ® 1,   therefore
 358
Evaluate the limit
Solution:   Let rationalize the numerator,
 359
Evaluate the limit
Solution:   Let rationalize both the numerator and denominator,
Evaluating trigonometric limits
 We use the fundamental limit and known trigonometric identities when solving trigonometric
limits.
 360
Evaluate the limit
 Solution:
 361
Evaluate the limit
Solution:   Since  cos(a + b) = cosacosb - sinasinb   then   cos2a = cos2a - sin2a = 1 - 2sin2a
 that is
 362
Evaluate the limit
Solution:   We use the sum to product identity and the fundamental trigonometric limit, thus
 363
Evaluate the limit
Solution:   If we substitute  arcsin (x + 2) = t   then,
x + 2 = sin t  or  x = sin t - 2  so that,   t ®as x ® -2,  therefore
Solved problems contents - A