Search & Filtering
Limit x approach infinity x[ ( 1 + a/x )raise to power of 1+1/x - x raise to power of -1/x ( x+ a ) ]
Selected values of the function f are shown in the table below. the function f is continuous on the closed interval [-2,2] and differentiable on the open interval (-2,2). Determine the validity of the following statement: there exists a value x in the open interval (-2,2) such that f'(x)=0. x: -2, -1, 2 and f(x): -10, -13, -10
Given the function f(x)=-x^3+3x^2+8, determine the absolute minimum value of f on the closed interval [-2,4].
EXAMPLES OF VECTOR CALCULUS IN REAL LIFE AND IN ENGINEERING
Find dy/dx and d²y/dx² without eliminating the parameter.
a.) x= acosh(t) , y= bsinh(t)
b.) x= acos(t) , y= bsin(t)
Prove that the Fibonacci sequence {fn}∞n=1 defined in Lecture 7-8 has the following formula: 1+√ fn+1 := 2 n 5 √ n 5 −1−√ 2 5 (n ≥ 0)
Write a formula for the an in each of the following sequences {an}∞n=1 given by (i) 2,1,4,3,6,5,8,7,... (ii) 1, 3, 6,10,15,... (iii) 1, −4,9,−16,25,−36,... Which ones among these are the subsequence of {n}∞n=1?
If x and y are arbitrary real numbers with x < y, prove that there exists at least one irrational number z satisfying x < z < y, and hence infinitely many.
Is the sum or product of two irrational numbers always irrational?
