(a) Prove and verify that the gradient of the tangent line to the curve f(x) = V5x² + 3x – 1 at (1,1) is V7. 23 14 (b) Limits of functions are evaluated using many different techniques, such as recognizing a pattern, simple substitution or using algebraic simplification. Evaluate lim x 3x-4x²+2x 5x (c) Express (x²+x+1)(x-2) as a Partial fraction, hence or otherwise show that the given expression can be deduced as 5(-2x+1) 7(x+x+1) 10 7(x-2)
(a) Prove and verify that the gradient of the tangent line to the curve f(x) = V5x² + 3x – 1 at (1,1) is V7. 23 14 (b) Limits of functions are evaluated using many different techniques, such as recognizing a pattern, simple substitution or using algebraic simplification. Evaluate lim x 3x-4x²+2x 5x (c) Express (x²+x+1)(x-2) as a Partial fraction, hence or otherwise show that the given expression can be deduced as 5(-2x+1) 7(x+x+1) 10 7(x-2)
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:Question 2
(a) Prove and verify that the gradient of the tangent line to the
curve f(x) = V5x2 + 3x – 1 at (1,-1) is V7.
23
14
(b) Limits of functions are evaluated using many different techniques, such
as recognizing a pattern, simple substitution or using algebraic
simplification. Evaluate lim
X→∞ 3x-4x2+2x
5x
(c) Express
(x2+x+1)(x-2)
as a Partial fraction, hence or otherwise
show that the given expression can be deduced as
5(-2x+1)
10
7(x2+x+1)
7(x-2)
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