Statement II is not a correctUse binomial theorem ( a − b) 2 = a 2 − 2 a b b 2 to expand ( x − 2) 2 fx=9\left (x^ {2}4x4\right) ∣ f ∣ x = 9 − ( x 2 − 4 x 4) To find the opposite of x^ {2}4x4, find the opposite of each term To find the opposite of x 2 − 4 x 4, find the opposite of each term fx=9x^ {2}4x4Now suppose that x1,x2 ∈ Z and f(x1) = f(x2) Then x1 5 = x2 5 and thus x1 = x2 It follows that f is onetoone Consequently, f is a bijection Notice that if a function f X → Y is a onetoone correspondence, then it associates one and only one value of y to each value in x In particular, it makes sense to define a reverse function
Solved Question 1 Let F X Sin 1 X 2 Then The Second Derivative At X 1 F 1 Equals A 2 3sqrt3 B 1 4sqrt3 C 2 Sqrt39 D Sqrt6 9 E Course Hero
Let f(x 1/x)=x^2 1/x^2 then f(x) is
Let f(x 1/x)=x^2 1/x^2 then f(x) is-It has been provided or mentioned that a function F(x1)=x^2–3x2 Interestingly, if we substitute a value of x1 in the place of x, we obtain, F((x1)1)=F(x) Therefore, F(x)=(x1)^2–3(x1)2=x^2–2x1–3x32=x^2–5x6 Hence, the function F(x) canM 2, and M 3 be metric spaces Let gbe a uniformly continuous function from M 1 into M 2, and let fbe a uniformly




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2) If fn → f uniformly on E, then fn → f pointwise on E The sequence f n ( x )= x n on 0 , 1 discussed in Example 1 of the previous section shows thatStatement II is a correct explanation of Statement I (c) Statement I is true, Statement II is true;1 1 and a = b = 2, then we see that a (b ~u) = 2 2 1 1 = 2 4 4 = 16 16 while (ab) ~u = 4 1 1 = 8 8 so we see that a (b ~u) 6= ( ab) ~u (c) V is the set of functions from R to the positive real numbers that is, V is the set of functions f with domain R such that f(x) > 0 for all x 2R Let f and g be in V We de ne f g and c f by de ning
(b) Pick = 1 Given any >0, pick x>0 such that 3 x2 2 >1 Then d(x 2;x) < but we have d(f(x 2);f(x)) = j(x 2)3 x3j= j 3 x2 2 3 2x 22 3 23 j 3 x2 2 >1 This shows that f(x) = x3 is not uniformly continuous on R 445 Let M 1;If f (x) = x1/x1 then find the value of f (2x) Find the answer to this question along with unlimited Maths questions and prepare better for JEE examination31 Continuity 23 so given ϵ > 0, we can choose δ = √ cϵ > 0 in the definition of continuity To prove that f is continuous at 0, we note that if 0 ≤ x < δ where δ = ϵ2 > 0, then f(x)−f(0) = √ x < ϵ Example 38 The function sin R → R is continuous on R To prove this, we use the trigonometric identity for the difference of sines and the inequality sinx ≤ x
Distinct solutions c 1;c 2 and c 3 and nally once more to conclude that f000(x) = 0 has at least two solutions d 1 and d 2 Next, note that since f is a quartic polynomial, f0must be a cubic, f00must be a quadratic and f000must be a linear polynomialWe therefore have a linearX0= 2 1 1 3 x et t 1 This becomes the equations x0 1= 2x x 2 tet x0 2= x 1 3x et 9416 Determine whether the given vector functions are linearly dependent or independent on the interval (1 ;1) sint cost ; Explanation By definition of the derivative f '(x) = lim h→0 f (x h) − f (x) h So with f (x) = 1 x2 we have;




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Let f (x) = (x 1)2 1, x ≥ 1 Statement I The set {x f (x) = f1(x)} = {0, 1} Statement II f is a bijection (a) Statement I is false, Statement II is true (b) Statement I is true, Statement II is true;Let f x = x x then f '0 is equal to1 0 1 2 Please scroll down to see the correct answer and solution guideOf course, the simple answer would be to just write ( x − 2) for every x you see The answer would be f ( x − 2) = ( x − 2) 2 − 3 ( x − 2) 1 f ( x − 2) = x 2 − 4 x 4 − ( 3 x − 6) 1 f ( x − 2) = x 2 − 4 x 4 − 3 x 6 1 f ( x − 2) = x 2 − 7 x 11




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Sin2t cos2t We compute the Wronskian det sint sin2t cost cos2t = sintcos2t sin2tcost= sint where the last step can be deduced byAnswer to Let f(x) = (x^2 3x 5)(sqrt(x) 1/fifth root of x) Find f'(x) By signing up, you'll get thousands of stepbystep solutions toGiven a function g with this property, we can easily construct a suitable f Just let f ( x) = { g ( x) x ≥ 0 g ( − x) x < 0 If g is additionally continuous then so is f We can find a lot of continuous g Pick a 1 ∈ ( 0, 1), let a 0 = 0 and recursively a n = a n − 2 2 1 for n ≥ 2




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Get an answer for '`f(x) = x/(x^2 1)` (a) Find the intervals on which `f` is increasing or decreasing (b) Find the local maximum and minimum values of `fLet p ∈ Z be any prime We will show that hx2 1i is properly contained in hx2 1,pi which is not equal to Zx This will prove that hx2 1i is not maximal Since every nonzero element of hx2 1i has degree at least 2, p 6∈ hx2 1i This proves that hx2 1i is properly contained in hx2 1,pi Now suppose, for the sake of contradiction, that hx2 1,pi = ZxIf we look at the behaviour as x approaches zero from the right, the function looks like this \begin{matrix}x & f(x) = \frac{1}{x^2} \\ 1 & 1 \\ 01 & 100 \\ 001 & \\ 0001 & \\ & \end{matrix}



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X Well begun is half done You have joined No matter what your level You can score higher Check your inbox for more details {{navliveTestEngineeringCount}} Students Enrolled {{navliveTestMedicalCount}} Students Enrolled Start Practicing6041/6431 Spring 08 Quiz 2 Wednesday, April 16, 730 930 PM SOLUTIONS Name Recitation Instructor TA Question Part Misc 6 Let f = {("x, " 𝑥2/(1𝑥2)) x ∈ R } be a function from R into R Determine the range of f f = { ("x , " 𝑥2/(1𝑥2)) x ∈ R } We find different values of 𝑥2/(1 𝑥2) for different values of x Domain Value will always be between 0 & 1 We note that Value of range



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