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Talk about the relation between differentiability and continuity on a real function and its derivative.

In a real 2-Dimensional function f(x) on the X-Y plane, we have the following relations between these concepts: i) f'(x) is continuous if and only f(x) is differentiable; in fact, the continuity of f'(x) ens...
MM
2700 Views

Differentiate x^3 + y^4 = 34 using implicit differentiation

An implicity function is one that is not expressed in the form y = f(x) such as the equation in the question. Instead of rearranging the equation to make y the subject, the equation can be differentiated usi...
OM
Answered by Olavo M. • Maths tutor
2624 Views

Given h(x) = 9^x + 9 and g(x) = 10*3^x, find {x | h(x) < g(x)}.

This question is asking to find the values for x, such that h(x) is strictly less than g(x). We can write this as 9^x + 9 &lt; 10 3^x and solve for x as follows. 9^x + 9 &lt; 10 3^x =&gt; 3^(2x) - 10 3^x + 9...
CM
Answered by Carlo M. • Maths tutor
4041 Views

Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.

Consider the Left-Hand-Side (LHS) of the equation first. LHS: 1/2 + 1 + 2 + 2^2 + ... + 2^10. We identify this as a geometric series by noticing that dividing any term u_(n+1) by the preceding term n the res...
CM
Answered by Carlo M. • Maths tutor
4241 Views

Find the area under the curve of f(x)=4x/(x^2+1) form x = 0 to x = 2.

Solution of all integration problems starts with investigation of a given function. We can’t represent it with standard functions, i.e. linear, power or trigonometric. Second step would be to try substitutio...
ID
Answered by Igors D. • Maths tutor
6097 Views