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If y = sec(z)tan(z)/sqrt(sec(z)) then find the indefinite integral of y with respect to z.

Using the substitution u = sec(z)=> du = sec(z)tan(z) dz.So, the integral ∫ y dz = ∫ sec(z)tan(z)/sqrt(sec(z)) dz=> ∫ y dz = ∫ 1/sqrt(u) du = 2sqrt(u) + C = 2sqrt(sec(z)) + C.

Answered by Jordan M. • Maths tutor

6366 Views

Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.

First, you will need to differentiate the function with respect to x. Finding dy/dx.For polynomials, this is done by taking one away from the old power and multiplying the coefficient by the old power and...

Answered by Laurence H. • Maths tutor

7749 Views

Integrate the function f(x)=3^x+2 with respect to x

First note that a=e^ln(a) and ln(a^b)=bln(a)By substituting a=3^x we get a=3^x=e^{ln(3^x)}=e^xln(3), and hence f(x)=e^xln(3)

Answered by Christian C. • Maths tutor

2756 Views

Find the maximum value of 2sin(x)-1.5cos(x)
Put the equation in the form Rsin(x-a) (=Rsin(x)cos(a)-Rcos(x)sin(a)). Looking at the original equation Rcos(a) = 2 and Rsin(a) = 1.5. Tan(a)=1.5/2 and R^2= 2^2 +1.5^2. Therefore R = 2.5 and a = 0.6435.Th...
TA
Answered by Tom A. • Maths tutor
7273 Views

Given that y = cos(3x)cosec(5x), use the product rule to find dy/dx.
Write out the product rule: if y=f(x)g(x) where f and g are functions, dy/dx = f'(x)g(x) + f(x)g'(x)
Substitute in the expressions from the question:Therefore if f(x)=cos(3x) and g(x) = cosec(5x), f'...
HL
Answered by Harry L. • Maths tutor
3244 Views

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Top answers

If y = sec(z)tan(z)/sqrt(sec(z)) then find the indefinite integral of y with respect to z.

Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.

Integrate the function f(x)=3^x+2 with respect to x

Find the maximum value of 2sin(x)-1.5cos(x)

Given that y = cos(3x)cosec(5x), use the product rule to find dy/dx.

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