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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) ...

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 ...

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 < 103^x and solve for x as follows. 9^x + 9 < 103^x => 3^(2x) - ...

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 ...

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 substitu...