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In what instances should the subjunctive be used?

The subjunctive is used to express wishes, emotions, impersonal expressions, doubt/denial and ojalá. To remember these siutations, the acronym WEIRDO is very helpful. Examples of impersonal expressions inclu...
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Answered by Gabriel O. • Spanish tutor
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What's the difference between 'por' and 'para'?

'Por' and 'para' both usually translate into English as 'for'. There is no firm distinction between the two so it is necessary to learn when you would use either 'por' or 'para'. Por: Duration of time e.g. T...
Answered by • Spanish tutor
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Evaluate the indefinite integral when the integrand function is tan(x).

To solve this problem we will use a clever substitution to easily integrate and thus obtain the answer.First we can represent tan(x) as its fractional equivalent sin(x)/cos(x), assigning the variable u to co...
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Using Pythagoras' theorem, show that sin^2(x)+cos^2(x)=1 for all x.

Take a right angled triangle with hypotenuse of length 1, and angle at the bottom of the hypotenuse equal to x. We will let o denote the length of the side opposite the angle, and a denote the length of the ...
Answered by • Maths tutor
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Given x = 3sin(y/2), find dy/dx in terms of x, simplifying your answer.

The first step is to find dx/dy in terms of y, which when differentiating comes out as 3/2cos(y/2), so dy/dx in terms of y is the reciprocal of this.The next step is to eliminate the y dependent terms, which...
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Answered by Max A. • Maths tutor
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