(g) Find the value of a and b such that the following limit exists. if x < 0, if 0 < x < 2, if x > 2. a cos x + 1 sin(5r) x2 – x + b f(x) = -

Q: 0 < x < 2. Let f(x) eCos T sin a < x < 27 2 Let g(æ) = f(s)ds = Ss T Find g and g(27). 2

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Q: Show that the functions f and g are identically equal.

A: Given functions are -  f(x) = sin x . tan x g(x) = sec x - cos x We have to show that f and g both…

Q: For which of the following intervals is the function f (x) throughout the interval? = cos (Tx) + 3…

A: Given query is to find the interval for which function is decreasing.

Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: Show that the extreme values of f(x) = a sin x + bcos x tVa2 + b2. are

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Q: 3. Find all values of a, b, c so that the following function is continuous for all values of x x-1…

A: Please see the below picture for detailed solution.

Q: Show that the functions f and g are identically equal.

A: We have  fx=cosx.cotx and gx=cscx-sinx Then, fx=cosx.cotx=cosx.cosxsinx=cos2xsinx And…

Q: Use sum and constant multiple rules to differentiate the functions, indicate where the rules are…

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Q: 16. Evaluate ft tan5 x sec¹ xdx.

A: We know that Sec²x = 1+ tan²x ∫ xn dx=( xn+1)/(n+1)

Q: sec? r da = F(x)

A: Given- ∫0π4sec2xdx=Fxab To find- The value of Fx Identity Used- ∫sec2xdx=tanx

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: Show that if L{f(t)} = F(s) then L{etf(t)} = F(s - k) where k is a constant. Hence find: (a) Leat…

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Q: Which of the following could be true if f'(x) = -x O f"(x) = 3 f"(x) = 4x f(x) = -æ O f(x) = -x

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Q: Find f g h. f(x)= 10x-1 g(x) = sin x h(x)=x² fog.h= Please answer all parts of the question. fog.h=…

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Q: Let f(x) = sin(rx). Suppose that h and k are two functions such that H (x) = cos(xx), k'(x) = f(x+…

A: Given that fx = sinπx . Also given that h and k are two functions such that h'x = cosπx , k'x = fx+1…

Q: 6. Determine the intervals on which the following function is increasing or decreasing f(x) = sin r…

A: Note here we need a interval to find out where function increasing and decreasing because it is a…

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

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Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given

Q: Find A and B if the function 3 sin? (4x) sin(6x²) if x 0.

A: