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What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?

First, we must find the value of y when x = 2.

y = x³+4x+5 = (2)³+4(2)+5 = 21

Then we must find the gradient of the tangent line. This can be done by d...

Answered by Oliver T. • Maths tutor

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A circle C with centre at the point (2, –1) passes through the point A at (4, –5).....

(a) Find an equation for the circle C.

Before tackling a question like this it is always a good idea to draw a rough sketch of all the information that's given to you.

Answered by Brodie W. • Maths tutor

17849 Views

Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.

To find the value of R, use Pythagoras's Theorem using the coeffecients of cos θ and sin θ. The correct answer should be R=5. Expand the expression R cos(θ – α). Equate the expanded expression with 3 cos...

Answered by Anahita G. • Maths tutor

22822 Views

How do I use the product rule for differentiation?

The product rule is a rule for differentiating products of expressions, i.e. 2 expressions multiplied together.

The rule is: if y=AB, then dy/dx=AdB/dx +B*dA/dx. This can be rem...

Answered by Thomas E. • Maths tutor

8284 Views

How do I evaluate composite functions?

Suppose you have 2 functions: f(x) = 3x², g(x) = log₃(x). These are arbitrary, any functions would work. Evaluate f(g(x)): let y = log₃(x) ( = g(x) ), then f(g(x)) = f(...

Answered by Seb G. • Maths tutor

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