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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...

Answered by Roberta M. • Italian tutor

1662 Views

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 w...

Answered by Thomas L. • Maths tutor

4898 Views

'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 ...

Answered by Eleanor S. • Geography tutor

11803 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 ve...

Answered by Oscar P. • Physics tutor

3334 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 enzy...

Answered by Yasmin T. • Biology tutor

3144 Views