Let f(x) be a differentiable function satisfyingf(x+y)=f(x)+f(y)∀x,y∈Randf′(0)=1.Then Lim_(x rarr0)(2^(f(tan^(2)x))-2^(f(sin^(2)x)))/(x^(3) f(sin x)) equals View Solution Let a real valued function f satisfyf(x+y)=f(x)f(y)∀x,y∈Randf(0)≠0...
Class 12 MATHS Let `f: R rarr R` be a differentiable fu...Let f:R→R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x2y+xy2 for all real numbers x and y. If limx→0f(x)x=1, then The value of f(9) is...
If | f(w) - f(x)| <=|w - x| for all values w and x and f is a differentiable function, show that -1<= f(x)<= 1 for all x-values. Show that the function is differentiable by finding values of ? 1 and ? 2 that satisfy this definition....
Let u be a differentiable function of x. Use the fact that |u|=u2 to prove that ddx[|u|]=u′u|u|,u≠0. Derivative and Use of the Chain Rule: If we have two functions y=f(x) and x=g(t), then the derivative of dydt ...
If F(x) is a differentiable function such that F(x)=f(x),∀x>0 and f(x2)=x2+x3, then f(4) equals Q. Let f:R→R satisfy the equation f(x+y)=f(x)⋅f(y) for all x,y∈R and f(x)≠0 for any x∈R. If ...
Answer to: Let A = \{1, 2, 3 \}, B = \{4, 5, 6, 7 \} and let f = \{(1, 4), (2, 5), (3, 6) \} be a function from A to B. Show that f is one-one. By...
THEOREM (Piccard's Existence Theorem). Let f(x, y) be a continuous real–valued function on the interval ! = [-a, a] × [-b, b]and let f satisfy a Lipschitz condition with Lipschitz constant L on !. Then there is a # > 0 with # < a and there is a unique function $(x...
Let {eq}f(x)=x^3 + x - 1 {/eq}. Find ech number c in (1,2) that satisfies the conclusion of the Mean Value Theorem. Mean Value Theorem If a function is continuous and differentiable over an interval, then we can apply the Mean Value ...
Let z0 ∈ ℂ and suppose f(z) is a complex-valued function defined on open disk containing z0. We say f is differentiable at z0 if lim f(z)-f(z0)/[z-z0] as z ->z0 exists. If this limit exists then we wrtie f'(z0) = lim f(z)-f(z0)/[z-z0] as z-> z0 Differenti...
If f has a derivative at x, what is the continuous linear transformation L : R → F and what is the map θ that satisfy Equation (12.1)? THEOREM 12.1. Suppose f : D → F is differentiable at a point x. Then both the continuous linear transformation L and the map θ of Equation ...