-) For the function f(t) = 16t3 - 40t consider the definite | integral "f(t)dt -1 a) Evaluate this integral; b) Find all values of x for which the integral becomes zero. Justify your answer.

Q: g(x) 1 -1 g(x) X 1 y y X g(x) 1 g(x) X 1 2 (c) Where is f differentiable? (Enter your answer using…

A: The given graphs are of f(x) and g(x). Here, note that the graph of a differentiable function has a…

Q: Find the values of a and b that makes f continous everywhere if  f(x) =

A:

Q: Apply Rolle's theorem for the function f(x)-x2+2x over the interval [-2,0]. Justify your answer.

A: Rolle's theorem is used to prove the Taylor's theorem and the mean value theorem. Rolle's theorem…

Q: Identify and sketch the domain of f(x, y) = 4x² In x Y

A: For function to be valid denominator must be non zero and log has non-negative real numbers and…

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Estimate L4 and R4 and over [0,7] for the function f(x) = 7x2

A: We have to estimate L4 and R4 in the interval 0,7 for the function: fx=7x2 L4 and R4 denote the left…

Q: Estimate L4 and R4 over [0, 7] for the function f(x) = 5x². (Use decimal notation. Give your answers…

A:

Q: b) Find out whether the following functions are odd, even or neither: i. 2x-5x+7 ii. x'+x*

A: Given:i. 2x5-5x3+7ii. x3+x4

Q: The domain of the function fod- tanh(17-) is (A, 198), Then The value of k- The value of A=

A: Let us consider the given function f(x)=tanh-1x The domain of the function is  x∈(-1,1) The range of…

Q: The slope of the line tangent to the graph of f(x) = 18 – 5x² at the point x = -8 O 20 O 10 O 160 O…

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Q: Use bisection and false position to locate the root of f(x)=x¹0-1 between .x = 0 and 1.3.

A:

Q: Evaluate the function 4" when x = {1, 2, 3, 4, 5}. x input y output 1 2 3 4

A: A

Q: Verify Rolle's theorem for the function 2x2 – 18x + 29 on the interval f(x) = [2, 7].

A: Given,          The function is fx=2x2-18x+29 on the interval 2,7.