ex – 1 Evaluate: lim x+0 sin-x A none of the given choices (B В does not exist C D 1 E 2

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A: In the given question we have find the limit of the function of two variable s.t…

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Q: Which of the following is not true? A Sin(x²)dx= limin(x²)dx c (B) None of the given choices .5 dx ©…

A: Given:  A)∫0elnx2dx=limc→0+∫celnx2dx B) None of the given choices C) ∫05dx25-x2=limc→5-∫0cdx25-x2 D)…

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Q: ´tan 3x sin 2x x#0 P] (4) Consider the function f, given by f(x) = x= 0 (For parts a and b) Evaluate…

A: Limits

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Q: sec x-cos X lim equals (A) 0 1 (B) (C) 1 (D) 2 (E) none of these

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A: We need to evaluate (∞/∞) form  and we use the fact  sin(∞) = oscillating number between -1 to 1

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A: The above figure shows the graph of function f(x), find the following: (a) f(1)(b) lim f(x)x→1(c)…

Q: e* – 4 , x< 3 - Let f(x) =- cos(x) %3D x2 3 lim f(x) = x 3 O DNE e3 – 4 - O 3 O cos (3)

A: Here we have to find the limit value.

Q: If g(x) = Cos x – Sin x a) Find g() and g (#) 8 b) Show that g ( - + x) = g(n – x) .2

A: sin(π2+x)=cosx cos(π2+x)=-sinx sin(π-x)=sinx cos(π-x)=-cosx

Q: suppose f(π/3)=4 and f'(π/3)=-5. Let g(x) = f(x) sin(x) and h(x) = cos(x)/f(x). Find the following…

A: Known facts: fg'=fg'-gf'fg'=gf'-fg'g2   Given that f(π/3)=4 and f'(π/3)=-5. Obtain the derivatives…

Q: Select the best answer. (2e + 1)= lim (tan(x))- O DNE O -00

A: We have to find out limit

Q: * /Q3 e*-(x+1) lim X→0 CoSx-1 %3D -1 1 -2 O O O O

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Q: Find the derivative of.

A: To determine the derivative of the quotient

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A: Given f(x)=√x and g(x)=3√(5-x)

Q: Let a be a constant. Evaluate L (* +2² + a) sin(8=") + 9=*)dz. -2

A: It is given that I=∫-22x4+x2+asin9x3+9x2dx Re-writing the given integration as I=∫-22x4sin9x3…

Q: For each natural number nonzero n we consider the function fn: [0,1]→ R: fn (X) ex 1+xn show that…

A: We have to use properties of integration here.

Q: 21. If f(x) = (x² + 1) tan-(e*), then f'(0) = (A) 0 (B) - (C) (D) 1 e

A: It is observed that the function fx=x2+1tan-1ex is a product of 2 functions x2+1 and tan-1ex.…

Q: ax + sin? y Let a be a nonzero constant such that a 89. Let f(x, y) : and let 89r? + y² L = lim(z,)…

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Q: Given f''(x) = – 9 sin(3x) and f'(0) = – 6 and f(0) = – 6. %3D - (5) = T Find f Add Work

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Q: ex – 1 Evaluate: lim x-0 sin-lx A 2 B does not exist © none of the given choices D E 1

A: To find the limit.

Q: Given f''(x) = 36 sin(6x) and f'(0) = 0 and f(0) = 2. %3D - (;) = T Find f

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Q: I 3 r 2 T 3.Evaluate 2 [2 sin x] dx = , where [] is define the greatest integer function.

A: Integral

Q: How would this Calculus problem be solved?

A: Given -5cos(πx)≤h(x)≤x5-1x-1 Using the Sandwitch theorem of limit…

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Q: e sin a – x lim 10 10 cos x- 10 O - 0.2000 | O 0.1000 O - 0.1000 O 0.2000

A: Use L hospital's rule as it of indefinite form. So differentiate the numerator and denominator both…

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Q: 2) Use the figure to give approximate values for the following (if they exist). Enter your answer as…

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Q: lim x" sin is NOT zero when: x→+∞ O a 1 a > 1

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Q: ex – 1 Evaluate: lim x-o sin-lx A B none of the given choices 2 D 1 E does not exist

A: To find:-

Q: ex – 1 Evaluate: lim x+o sin-x A none of the given choices B 2 1 (D does not exist E)

A:

Q: Q2) A: If u = sin-()+ tan-(), prove that du ди x=+y дх ду = 0 ax ay n lim (1+ (1 + iV3)10 B: Find:…

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Q: If g(x) = Cos x- Sin x 7T a) Find g) b) Show that g + x) = g(n – x) and g () 8. %3D

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Q: ex – 1 Evaluate: lim +o sin-x (A B 1 D none of the given choices E does not exist

A: It's interminnate form  Apply L hospital rule

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Q: lim-sin t t0 In(2et_1) %3D A © D B.

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Q: ex – 1 Evaluate: lim x+o sin-1x (A does not exist B) 1 D E) none of the given choices

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Q: 2. Given that the function f(0) = a sin (be) has exactly 5 zeros for 0 ≤ 0≤ 2, it is possible to…

A: Above question is solved.

Q: 1+sin(x) lim is p ritoc 9. O alon13 (A) 0 (B) 1 (C) 2 (D) TT 00

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Q: Q3// Answer the following (20 mark): А. Vx+5-3 1. lim x-4 x-4 x+x cosx 2. lim x-0 sinx cosx

A: