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Let f be a function defined in the interval (1,\infty) as f(x)=\integral_{e} ^{x^2} t/ln(t) dt. Find the equation of the tangent line to the graph of f at the point whose x-coordinate is sqrt{e}.

The equation of the tangent line to the graph of the function y=f(x) at the point whose x-coordinate is sqrt{e} is given by y-y f =m(x-x f ), where x f =sqrt{e}, y f =f(sqrt{e})=integral_{e}^{e} t/ln(t) dt =...
RM
Answered by Roberta M. • Italian tutor
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Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2

First, use the identity cos(2x)=(cos(x))^2-(sin(x))^2 along with the identity (sin(x))^2+(cos(x))^2=1 to obtain the integral of 1/2*(1-cos(2x)) as it is not possible to integrate (sin(x))^2 straight off with...
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Answered by Thomas L. • Maths tutor
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'Physical factors play a more important role in the spread of disease than human factors'. Discuss.

Firstly, it is important to acknowledge the 'discuss' phrase in the question. This implies you need to evaluate both physical and human factors, and their role in the spread of disease, before ultimately dec...
ES
Answered by Eleanor S. • Geography tutor
12509 Views

If a ball is launched at ground level at a velocity v and angle θ, find an expression for it's height at horizontal distance x.

Firstly it must be understood that vertical and horizontal motion can be treated as independent, as they are perpendicular to each other (and acceleration due to gravity only affects the y component of veloc...
OP
Answered by Oscar P. • Physics tutor
3774 Views

What is the effect of temperature on enzyme activity?

As temperature increases, the enzyme activity increases since the particles have more kinetic energy and collide more frequently; with a greater proportion of the collisions being successful and more enzyme-...
YT
Answered by Yasmin T. • Biology tutor
3861 Views