PLEASE TYPE ANSWER IF HANDWRITING IS SLOPPY. PLEASE WRITE LEGIBLY!!!!!!!!!!!!!!!
Posted: Wed Jul 06, 2022 11:50 am
PLEASE TYPE ANSWER IF HANDWRITING IS SLOPPY. PLEASE WRITE LEGIBLY!!!!!!!!!!!!!!!
6. Use the rule of inference "If A implies B, and B implies C, then A implies C." to prove the following statements: (a) If f(x) and g(x) are continuous functions on R, then lim g(f(x)) = g(ƒ(0)). x-0 (b) Let A be an n x n real matrix. If x € R" is a nonzero vector such that Ax singular (i.e. non-invertible). 0, then A² is
Use the rule of inference "If A implies B, then not B implies not A." to prove the following statements: (a) If an integer n is not divisible by 3, then it is not divisible by 6. (b) If vectors V₁, V2, V3 in R³ do not span R³, then they are not linearly independent.
Let x E R. Prove: If x < 5 and x ≥ −3, then (x-6)³ +1 <0.
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Use the rule of inference "If A implies B, then not B implies not A." to prove the following statements: (a) If an integer n is not divisible by 3, then it is not divisible by 6. (b) If vectors V₁, V2, V3 in R³ do not span R³, then they are not linearly independent.
Let x E R. Prove: If x < 5 and x ≥ −3, then (x-6)³ +1 <0.