Use e-ð to prove lim,1 sin x = sin 1. [Hint: we know sin(1 +h) = sin(1) cos(h) + cos(1) sin(h), which means sin(1 + h) – sin(1) = sin(1) · (cos(h) – 1) + cos(1) · sin(h). =-2 sin () Then use the fact (for free) that sin(x) < |x| for all x.]

Q: A- Say whether the function is even, odd, or neither 1) g(x) = 4+tan x 3) g(x) == .) f(s) = 3s +2 4)…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 4. Differentiate the following without simplifying f(x) = [4 cos cos (x)][√sin² (cosx)]

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Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = cos 2x

A: Given  f(x) = sin2x, g(x) = cos2x and h(x) = cos2x Then, we have to determine h(x) is in span(f(x),…

Q: ) Define the domain and range of f(x) where f(x) = sin²(x) – 1

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Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = 1

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A: Given, f(t) = sin(t+tan√t) + ln(2t+1) fl(t)=?

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Q: cos x lim z-n/2 sin (2x)

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Q: The derivative with respect to x of 2 cos (x² + 2) is A. 2 sin (x²+2) cos (x² + 2) -2 sin (x² + 2)…

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Q: Differentiate a $sin "(z) with respect to sin x.

A: We will find out the required value.

Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: sin(z)+9 cos(z)–9" Find the derivative of If you need to enter an expression like sin x with STACK,…

A: To find  The derivative of given expression.

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

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A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: 1. Differentiate the following functions a. f(x) = sin(x) cos(x)

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Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: by using mean value theorem prove |sin(x) – sin(y)I < ]x – y|

A: To prove sinx-siny≤x-y Let f(t)=sint ∀t∈(x,y) Then we have the mean value theorem f'(c)=f(x)-f(y)x-y…

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A: As question has many subpart we are giving solution for first three subpart. If you want solution of…

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Q: 1) Find the derivative of the following trigonometric expressions below. Please show all of you work…

A: A)y=sin x+ cos x -3x2dydx=ddx(sin x)+ddx(cos x)-ddx(3x2)dydx=cosx -sin x -6xB)y=-12…

Q: Find the derivatives of the given functions. Remeber to apply the product, quotient, or chain rule…

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