Answer to: Determine whether the statement, if a function is differentiable at point (a, f(a)), then f(x) is continuous at x = a, is true or false...
Answer to: Determine if the function g(x) = x + 1, x less than 1; and 2\sqrt{x}, x greater than 1 is differentiable at x = 1. By signing up, you'll...
If f is a differentiable function satisfying 2f(x)=f(xy)+f(xy),∀x,y∈R+,f(1)=0 and f'(1)=1ln6, then f(7776)= View Solution If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(xy)∀x,y∈R and if f(2)=5, then find the value of f(f(2)). Vi...
Determine if the given function is equal to the following f(x) = - csc(x - 2 \pi) + 2. Consider the following function: f(x) = csc(x - 9 \pi) + 2. Determine if the given function is equal to the following [{MathJax fullWidth='false' f(x) = - csc(x - \pi...
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a function is differentiable at a point, then it is continuous at that point. If f(x) = u(v(x)...
ATQ, f(x) is continuous at x=0 If f(x) is continuous at x=0, then $$ f(0)^{-}=f(0)^{+}=f(0) $$ $$ \begin{aligned} &\Rightarrow \lim {h \rightarrow 0} \cos (0-h) \\ &\Rightarrow \lim {h \rightarrow 0} \cos (-h) \\ &\Rightarrow \lim {h \rightarrow...
If the coefficient of .ω is an arbitrary differentiable function . (r) of the potential buoyancy, i.e., .δC/δω = (r), we have .∇ · r∇⊥ δC = ∇ · r∇⊥ (r) = (r)(∇r ·∇⊥r)+r(∇ ·∇⊥) (r) = 0, (22) δω An Explicit Method to ...
According to the well known calculus theorem, any differentiable function must be continuous at every point in its domain, in Wagner's deduction, J1 and J2 in the Eqs. (7), (8), (9a), (9b), (10), (11) must be continuous between λ = −∞ and λ = λ*, and between λ = ...
To estimate the curvature of nuclei along each point of their perimeter, we first fit fourth-order splines to the border of the binary masks using the “UnivariateSpline” function from SciPy python library (35), then evaluate Eq. 1 using the obtained differentiable curves. Blebbiness index ...
Find values of a and b such that the function: f(x) = x^2 +3x-3 if x less than or equal to 2 ax+b if x greater than 2 is differentiable at 2. For what values of x is the following function differentiable: f(x) = { x wher...