The piece-wise function g(θ) is given by g(θ) = { A sec2 θ + 1 : 0 < θ ≤ π/4             {2 tan θ + A : π/4 < θ < π/2

Q: Let 1(2) = sin(rz) (1- h)? + k :>: (a) Find values of h and k so that ƒ is a differentiable…

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Q: The temperature in degrees Celsius (C) in Toronto starting on March 1** can be represented by the…

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Q: The derivative of the function y = cot¬1(cscx) is: is: cSc X cot x y' csc x cot x y' csc²x+1 csc?x+1…

A: Find the derivative of the function

Q: + Vx + vx Q3: a) Differentiate b) Differentiate (Cosx)³tnx with respect to (Tanx)Secx ´with respect…

A: a)  f(x) = x+x+x      f'(x) = 12x+x+xd(x +x+x)dx             = 12x+x+x × (1+12x +x)×d(x+x)dx…

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: 2) Let f(x) be a differentiable function on the interval [gk]. What does the Mean Value Theorem tell…

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Q: Let f be a function defined on the closed interval -4sxs4. The graph of f', the derivative of f, is…

A: Let's find.

Q: The curve of a function f (x) is given in the figure below and you are asked to draw on it   a)…

A: The curve of the function f(x) is shown as,

Q: Compute the derivatives of the fallowing functions. use any rule but explain what ar methed, did No…

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Q: lutorial Exercise Find the point of inflection and discuss the concavity of the graph of the…

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Q: Find the derivative using suitable differentiation rules: + 3x + ¹) J- = 5x + sin(x² + 3x + 1)…

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Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: A fixed point of a function f is a value x where f(x) = x.Show that if f is differentiable on an…

A: Suppose fx be any function, then a fixed point of the function f(x) is a value of x  when fx=x Now,…

Q: a) Find the derivative of the following functions (i) y = x² sin* x + x cos-2 x. (ii) y = e(4vz+z²).…

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Q: 4 sin(3f(x))·f'(x) dx (c) Let fbe a differentiable function on the interval [a,b]. Compute/a . Note:…

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Q: Use a plot to argue that tan(x) is not differntiable at +or- π/2. b) Use the fact that d/dx…

A: In the following, we have proved that tan(x) is not differentiable at +or-  π/2.

Q: Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.…

A: We have to find

Q: Find all extrema and any inflection points for the function f(x)=sec² x-2 tan x on the interval T T…

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Q: Estimate f(5.03) for f as in the figure. y=f(x) (10, 4) Tangent line (4, 2) (Give your answer to…

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