In(x) sin (x – y) 2 lim ( π,υ) + (π,π/2) | Y – x lim (x,y)→(1,1) 1 – y + ln x

Q: (a) Let r(t) = (√√t² – 1, e¹t, ln(2t — 4)). (i) Find the domain of r(t). (ii) Find lim3 r(t). (iii)…

A: Step 1:Step 2:Step 3:

Q: (a) Sketch the graph of f(t) = sin 2(t- π)U(t - π).

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Example 7: Find lim sin(a+h)-sin in a h→0 h Solution // lim h→0 sin(a) cos(h) + cos(a) sin(h) –…

A: Step 1:Method1 Method2  Step 2: Step 3: Step 4:

Q: sin(2x) limy→ 0+ X

A: Given:     limx→0+sin2x2

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: If f(2010) = π/2, f(2x) = f(x)Vx E R and f(x) is continuous for x E R, then the value of…

A: Let us solve above problem by using L'Hopital rule

Q: b) lim (4-5 ln(x) +8e¹00-2) 14X

A:

Q: (a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

A:

Q: Let f(x) be a function f:[−1,1]→[0,1], f(x)=x^2. Let g(x):(−∞,∞)→[0,1] be a function such that g(x)…

A:

Q: f(x) = x+1 g(x) = log(102tan¹(x)), h(x) = x . 1) Find lim f([h(x)]²) X-1 2) For the following…

A: Step 1:Step 2: Step 3: Step 4:

Q: x²y" — xy' – 2y = 0.

A: Yes, a solution exists

Q: Calculate the difference quotient for f(x) = 5 – x² at a = 4. (Express numbers in exact form. Use…

A: