Consider the following functions. (a) f: R*→ GL2 (R), f(a) = 1) (b) ƒ: R* → GL₂ (R), f(a) = (i). a (c) f: GL₂(R)→R,ƒ (d) f: GL₂(R)→ R, f (e) f: GL₂(R) → +R*, ƒ ((ad)) f For each of these functions, answer the following questions, with a (brief) justifi a *((d)) ab. =a+d. = ad-bc.

Q: Differentiate. f(w) 1 + sec(w) 1 - sec(w)

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Q: consider a function f, defined by f(x,y) = -y/√x2+y2   what is the behavior of f along the line…

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Q: If f(a) = 7 and f(b) = 0, then there exists a number c in the interval (a, b) such that f'(c) 7 a –…

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Q: If h and f are functions and g defined by g(t) = f(t) · h(t), then what is g'(t)? f'(t)h'(t) +…

A: We have given that gt=ft·ht Differentiate the above function w.r.t 't' g't=ddtft·ht

Q: Suppose f: (a, b) →→ R is differentiable. True or false: If f is unbounded, then f' (the derivative…

A: f:a, b→ℝ is differentiable.

Q: 36. Let f be a twice-differentiable function of z such that, when z = c, f is increasing, concave…

A: We have given function of x which is twice-differentiable such that when x=c, f is increasing,…

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: |- Let f(x, y) = y²e* +y find fryy

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Q: Use the second derivative f"(x) = x(x+ 1)(x-3) to determine where the function f(x) is concave down.…

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Q: Are these functions injective or surjective?  f : R → R; f(x) = x^2,  f : R → Z; f(x) = bxc,  f :…

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: Suppose g and h are everywhere differentiable functions such that g(2) = 1, g' (2) = 2, h(2) h'(2) =…

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Q: 10. Let F(x, y) = 1 + v4 – y². (a) Evaluate F(3, 1). (b) Find and sketch the domain of F. (c) Find…

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Q: Let f be a function that is defined and differentiable on all of R. Here is some information about /…

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Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: a) f(x,y) = x³ + y³ + y(3x²y+ 3ry²) b) f(x,y) = x² + iy³

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Q: Let f(x, y) = √√/175 – 3x² – 4y² Evaluate f(1,4)

A: Given :To Find :

Q: dR/dt = a * R / (b + R) - c * R dS/dt = d - c * S (a,b,c,d are all constants) what is the…

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Q: The interval in which the function f(x) = 2x – 12x is decreasing is O a. (-0,0) O b. (-0,-4) O c.…

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: The function, r= 3t°, y =ť –t is concave upward on the interval (a) (-∞,0) (b) (0, 0) (c) (-0,0) (d)…

A: The general form of the parametric equation of the curve in two-dimensional space is given by…

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

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Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: 3. Suppose that f is differentiable on all of R and g(x) = f(x)². If the table below describes the…

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Q: dz (е) dz

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Q: f(x, y, z) = e−(x2+y2+z2) (a) Describe the domain of f. (b) Determine the range of f.

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Q: Let f (x) = vr +2² + 2 , ro = 1, h = 0.5, r1 using the Three-Point formulas to approximate f(1) (1);…

A: Given: The given fx=x3+x2+2, x0=1,h=0.5,x1=1.5 and x2=2

Q: F:(- 2, 2] → R, F(x) = [, (t- 3)(f² + 1) dt

A: Given, Fx = ∫-2x2t - 3t2 + 1 dtFx = ∫-2x2t3 - 3t2 + t - 3 dtFx = t44 - 3t33 + t22 - 3t-2x2Fx = x44 -…