Using the definition of the derivative, find f'(x). Then find f'(-4), f'(0), and f'(4) whenm f(x) = 3x +3 Find f'(x) using the definition of the derivative. f'(x) =|

Q: Prove that a non-empty subset U of R" is a subspace of R" if and only if U = Span(S) for some…

A: Question: Prove that a non-empty subset U of ℝn is a subspace of ℝn if and only if U=SpanS for some…

Q: The exponential function N = 3.93 x 1.34d gives the approximate U.S. population, in millions, d…

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Q: For each of the following matrices A: (i) find its rref R; (ii) find the rref R' of AT; (iii) find a…

A: Hello, Since there are multiple questions with multiple subparts. So we'll solve first question…

Q: If f(x) = sin(x³), find f'(x) Find f'(1)

A: See this solution in below.

Q: For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. p-8q 6p+7r…

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Q: Evaluate the integral 32 3 √2³ (2² (x² − 2) dx =x²-2. by making the substitution u = x² + C

A: We know, ∫xndx= xn+1/(n+1) +C, C is a constant and for any real number n. Let I=∫x³(x⁴-2)³²dx

Q: If f(x) = 5x4 - 2e, find: ƒ'(x) = f'(3)= f''(x) = f''(3) =

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Q: 5. Betweenness in taxicab geometry. Let A = (0,0), B = (1,0) and C = (1, 1) and let p denote the…

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Q: 6. Suppose that A is an n × n matrix. Prove that nullity(A) = nullity(A™).

A: Nullity (A)= Nullity(A^t)

Q: Solve the equation. 4 = 64 ...... What is an appropriate first step to solve for x? Select the…

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Q: 3. Prove or disprove: If a | (b + c), then either a |b or a | c. h of the follo

A: Since you have asked for question number 3 , we have solved it for you.

Q: Show that any integer of the form 6k + 5 is also of the form 3j + 2, but not conversely.

A: 2. We can write 6k+5 = 6k+3+2=3(2k+1)+2 lets write 2k+1=j hence 6k+5=3j+2