5. Let f : R -→ R be defined by f(x) = 2x +9. Find a formula for f-1.

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

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Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

A:

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

A:

Q: Suppose f(x) = - 2x - cosr. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: (5) Use the limit definition of derivative to prove the following: (a) For any a e R, (f(ax))' =…

A:

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

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Q: Please

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Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

Q: 16. Suppose that f is differentiable at c and that f'(c) + 0. Show that there exists a ð > 0 such…

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Q: on f(x, y) = 3x + 9y subject to th %3D

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Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: Find the linearization L(x) of f(x)=tan x at x=3pie/4.

A: Given

Q: For what values of a and b is ax + 2b, g(x) = {x + 3a - b, 0 2 continuous at every x?

A:

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: (Q4) Prove directly from the definition that the function f: R→ R defined by f(x) = 3r² +r for all r…

A: Sol

Q: 4 Given that f(2) is analytic at z = 0 and that f G) =, n = 1,2, 3..,find f(2). VE

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Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

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Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: Let f(x) = x²+x+ 2 = Z₂ (x) prove that f(x) irreduciable Poly

A: The given function is  f(x)=x2+x+2.

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: 1 - t Let F(x) = dt for -o << x < +∞ t2 + 24

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

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Q: f(z) = z2

A: We have to show the given function is not analytic at any point.

Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

A:

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

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Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

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Q: X if x e Q If f (x) is defined on [0,1] by the rule f (x) = < (1-x , if x 4 Q Prove that fof (x) = x…

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Q: The function f(x) =x + 1/x is concave upward on none O (-1) O (0,) O (0,1) O (1,)

A:

Q: Q2 Let f(x) = c x= 0,1,2,3, . 1-find c ? 2-find EX(X – 1) ?

A: Given a probability mass function; f(x)=c2xx!, x=0, 1, 2, 3, ... 1. We know that a very important…

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

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Q: 1 dt, for x > 4. In(t) Let F(x) 4

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Q: Find the value of K that makes 4-x2 f(x) = {2-x if x # 2 2K if x = 2 continuous at x = 2 ?

A: Find the value of k

Q: (1- a? f(x) = 1– x² if x E Q, if r ¢ Q. %3D p at which f is continuous. Prove your conclusion.

A:

Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

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Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

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Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

A: