1. Solve the following initial value problem 3 1 0 1 *(t)= - ( ) ( ). - (1) -1 50 x(t) + x(0) = 0 0

Q: 2. Given f(x)=√x+1, g(x) = 3−*,h(x) = cosx, m(x) = log[-(x − 4)] and p(x) = ¹3 The equation in fully…

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Q: 1. (a) If f(n) = 0 (g(n)) then is g(n) = Q(f(n))? %3D

A: Big O, big Θ, and big Ω notations are very important in studying the time complexity and asymptotic…

Q: d²x 4. + xe0.01x = 0. JP x(0) = 1, x'(0) = 1; x(0) = 3, x'(0) -1

A: Given that d2xdt2+xe0.01x=0, x0=1,x'0=1; x0=3,x'(0)=-1. (i) So, the equation can be written as,…

Q: If h(x) = f (g(x)), where f(0) = 7, g(0) = - 1, f'(0) = 0, g'(0) = - 3, f(- 1) = - 3, g(- 1) = 2,…

A: We have hx=fgx

Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

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Q: If f(x) = g(h(3x)), then f'(x) is equal to which of the following? Og'(h '(3x)) Og'(h(3x))h (3x)-3…

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Q: Find the equation of the tangent link to f(x)=x³+x²+x @x=3 A y=34x-63 B D y=-12x-36 y=12x-36…

A: 20) The function is  f(x)=x³+x²+x  Note:- As per the rules, we are supposed to answer the first…

Q: If g(t) : 3t4 + 2t? – 7 find - g(0) g'(0) g''(0) : g'''(0) g(4) (0) (5) (0) ||

A: Given that, g(t)=3t4+2t2-7. Obtain the value of g(0). g(t)=3t4+2t2-7g(0)=3(0)+2(0)-7g(0)=-7 Obtain…

Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

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Q: The number of deaths among members of the U.S. Navy in the first 3 months of the 1918 influenza…

A: (a) Numerical estimation of N with increase in t.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: (1) Given functions are  f(x) = (2x2-1)(x2+3)x2+1  and g(x) = (x2+8)7(2-3x2)5

Q: 1, -1 X'=1 3 0 0 2

A: The given differential equation is  dXdt=1-1-1131002X The general solution is of the form…

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: 5. Consider the equations: det f(x) = A(1+)™* g(x) = A· ex and %D %3D For x =1 (a one year…

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Q: 16) g(x) = 4x - 5 s(x) = x' + x² Find (g + f)(-2)

A: Given,      g(x)=4x-5      f(x)=x3+x2

Q: E 40 (X) + (²²) (+) (A(+1) = 20₂² (e (t))

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Q: (vi) Suppose that capital expenditure varies with time in such a way that t months from now there…

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Q: *Problem 3.4 Suppose you start out with a basis (lei), le2), ..., len)) that is not orthonormal. The…

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Q: Can you explain to me starting at the sentence, "The denominator of the right hand side is larger…

A: The given fraction in the integrand is: R2-r2R2-2Rrcos ϕ-θ+r2 Explain why the denominator of the…

Q: If g (2) = 12 and g'(x) 2 for 2 <xS 6, what is the smallest value g(6) can be? Why?

A: To find the smallest value of g(6)

Q: 5. The height of a drone in metres over time in minutes is given by f(x) = 3 - log₂ (x - 1). The…

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Q: Find f'(x). f(x) = (x² + 1) * f"(x) = %3D

A: Find f''(x)

Q: 10. Use the given information to find f"(2) of the function f(x)=g(x)h(x). g(2)= 3 and g'(2)…

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Q: 7. The graph of a function f, which consists of two line segments and a quarter circle, is pictured…

A: As per the Fundamental theorem of calculus, the derivative of the given function  will be given…

Q: 1-3. Find the derivative of each of the following. In each case, simplify your answers as much as…

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Q: 1. Find the derivative of the following (a) f(x) = log-(r* +2) + 7** (b) k(r) = In(x) + 5e¯ (c) j(z)…

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Q: If f(1) = 5 and f'(x) > 2 for 1< x < 6, then the smallest value of f(6) would be

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Q: If g(t) = 1t¹ — 9t² – 3 find g(0) gʻ(0) = g''(0) = g'''(0) g (4) (0) g (5) (0) = = =

A: g(t)= t4-9t2-3

Q: d? 9. If g(1) = 2, g'(1) = 3, g"(1) = -1, S'(2) = 4, and "(2) = 3, then %3D

A: