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First we need to rearrange so that it's all on one side of the equals sign:x² + 2x - 48 = 0 Now we have to find what will sum to make the coefficient of x (2) and multiplies together to get -48...

Suppose f(x)=x²+4 and g(x)=3xg(f(x)) would therefore be 3(x²+4) and that equals 3x²+12the next step would then be to substitute x with 1 to find the solution for (g(f(1))....

a. Finding du_n = u₁ + (n-1)du₄ = u₁ + (4-1)d12 = 3 + 3dd = 3
b. Sum of first 10 termss_n = n/2(2u₁ + (n-1)d)s₁₀ = 5(6 + 9d)...

Formulae to be used: n^th term of an arithmetic sequence u_n= u₁ + (n-1)d and sum of the first n terms of an arithmetic series S_n = (n/2) * (2u₁ + (n-1...

Using the product rule H(X) = f(x)*g(x) and H'(X) = f'(x)*g(x) + f(x)*g'(x) Where, in this case f(x) = x³ and g(x) = e^x We can easily determine the derivative of the above function.f...