2t? – 3t Given that r(t)=| sin 2t j+ 3t k, find limr(t).

Q: =: Find L(sin(t)).

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Q: C. lim x→1+ 5x 4 31 -1-x 3x]

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Q: (d) lim 140 sin(2x) – sin(3x)

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Q: 20xth)t xth 3. Zx- Find the limi,t

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Q: Given h(x), find two functions fand g such that h(x) =(f•g)(x). a. h(x) =|2x° – 5| b. h(x) = /9- 4x

A: We need to find two functions f and g such that h(x) = (fog)(x). Note that there are many possible…

Q: Q1: Find A: fxx fyy and fxy for the following functions f(x,y)= In(tan-¹xy)

A: Let us consider the given function z=f(x,y) The first order partial derivative are ∂f∂x,∂f∂y The…

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

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Q: sin(x) 3h dr. Use the mid-point method | f(x)dr=[f (x0) + f(x1)] to evaluate (b) I-1

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Q: Let f(x) = (– 4x² + 3x – 6)ln(2a – 10). - Then f'(x) =

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Q: cos x lim Vx

A: Given: limx→∞cosx5x=?

Q: Find the values of a and b that makes the following function differentiable. S(2) – {3e¬3 la(6 – 2)²…

A: Given fx=3ex-3      if x<3a6-x2+b   if x≥3

Q: 5x C. lim 1-52, x→1+ -1-x 3x] D. Compute the derivtive of sin³ (x + 1)

A: Given: sin3x+1. We have to compute the derivative of the given function.

Q: f(x) A B = arcsin x, then lim 1/1/12 0 ㅠ 6 f(x)−ƒ( ² ) X→ X- 1|2 is

A:

Q: 4. Given f(x) = sin² (2x) find the slope at (5, 1) a)-√3 b) √3 d) 0.1395

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: IB) Find the cnber of curvatee, eguation of the curde of cuuunfure f (x)> Jax of the gmph. of at x=…

A: Consider the given curve as, fx=2x at, x=4 Let y=fx=2x

Q: Ex: Using U= x²-1 x²+1, find: 1 x² - 1 x² +1√1+x4 dx

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Q: Let f(x) = arctan + arccos (sin x), find and simplify.

A: Given function: We have to find  and simplify.

Q: If 4x<9(x) <2x-2x°+4 for alle x, evaluate lam g(x). Explain!

A: on solving this we get

Q: x2 + x – 6 lim Evaluate: z-2 x4 – 3x³ + 7x² – 15x + 10 9 А. 9. D. 5 5199 | 5 B.

A: topic - limits

Q: 4. Use the fplot command to plot the function f(t) lcos(3x)+ sin (4x) in the domain -25 x S2. %3D

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Q: Q5) Find the root of f(x)= 5 sin(x) + ex² by using bisection method take a= -1.25 and b= -1.0 for…

A: Given, fx=5sinx+ex2. Here, a=-1.25b=-1.0 Now,…

Q: (x²–x-2) (x³–2x-4) Evaluate limr→2 1 10 O None 3 10 7 10

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Q: -y . If f(x, y) is harmonic, show that f is x2 + y2' x2 + y2 also harmonic.

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Q: (sinx –) limx- (3sin²x –sinx +1) 21 7 →- 6. 2

A: Answer is -2.