sin z Prove that lim Cosz - = 1 and lim = 0. Z→0 Z Z→0 Z Hint: use the definition of the derivative, f'(0) = lim Z→O ƒ(z) – ƒ (0) Z

Q: Let f(x) = tan -(x). and g(x) = In (1 + x*). The tangent lines of f(x) and g(x) are parallel at what…

A: The tangent lines of f(x) and g(x) are parallel at some x where f'(x)=g'(x)

Q: Evaluate lim Δy→→0 sin(5y+Av)–sin(5y) Δι

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Q: Use the limit definition of the derivative (as demonstrated on the left) to compute the exact…

A: We have to compute f'(1) using the limit definition i.e. the derivative of the square root function…

Q: f(x) = 2+6x -x'use the limit definition of derivative t

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Q: Consider a quadratic function f(x) = ax?+ bx + c, where a, b, CER and a # 0. She hat the tangent…

A: f(x)=ax2+bx+climit definition of derivative states that :f'(x) =limh→0f(x+h)-f(x)hf'(x) =limh→0…

Q: Let f(x) = 19 – z It is required to use the limit definition of the derivative to find the slope.…

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Q: (d) VT tanr - 2 V lim /4 VT x(4x – 7) Hint: divide both parts of the fraction by VT x and represent…

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Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

Q: Use the definition ƒ'(zo) = lim Z→>>> ²0 1 derivative of f(z) == for z = 0. Z f(z)-f(zo) Z-ZO of the…

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Q: Consider the function h with criterion differentiable functions in R. Which of the following…

A: Using derivatives to find answer

Q: Use the definition of the derivative (that is, f'(a) = lim sec(x) da to compute h+0

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Q: Suppose f is differentiable with continuous derivative on [a, b]. Show that lim f(x) sin(nx) dr = 0.

A: To prove the given limit