Let f(x) = (2 - |x - 4|) / x. Find all values of x where f is not differentiable. Find f'(x) for the following functions. (a) f(x) = \sin^4(4x^5) (b) f(x) = g^n(\tan(x^2)), where g is a differentiable function and n is a constan...
Determine where {eq}f{/eq} is continuous. {eq}f(x) = \left\{\begin{matrix} \frac{sin (x)}{x} & x \neq 0 \\ 1& x = 0 \end{matrix}\right. {/eq} Limit It is the value that a function approaches as its input approaches to some value....
Consider a function f(x) which is differentiable, then the intervals can be determined where function is concave down and concave up. When the second derivative is strictly greater than zero, then f(x) is concave up and when the second der...
Determine whether f(x) = -2*sqrt(25 + x^2) is a one-to-one function. Find a function f that satisfies the conditions: f"(x)=x^2, f'(0)=8, and f(0)=8 Find a function f(x) that satisfies the equation f''(x) = 15 \sqrt x. Find f such that the given co...
The Hamiltonian is therefore a functional on the space .X∗( ) × V ∗( ), where .X∗( ) is the dual space of .X( ) with respect to .L2-pairing on . . For the thermal rotating shallow water model, the momentum is given by .m = η(u + R) and the Hamiltonian is .HT...
n calculus‚ Rolle’s theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. --- Standard version of...
Iff(x)is an even function, then write whetherf′(x)is even or odd. View Solution View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation ...
If f(x) = max(sinx, cosx) Vx e R. Then sum ofmaximum and minimum values of f(x) is M then find1M+1√2 View Solution Iff(x+y)=f(x)f(y)and∞∑x=1f(x)=2,x,y∈N, where N is the set of all natural numbers , then the value off(4)f(2)is : ...
where |A e | and μ(A(R i ), ∀i) are the numbers of manually counted erythrocytes in a cluster C i and the average area covered by an erythrocyte, respectively. The area function A(·) is defined as in Equation (10). The rationale behind the measure is to relate the actual ar...
The domain of a function is defined as the set of all {eq}\displaystyle x {/eq} values where the function exists. The range, on the other hand, are all the possible values of {eq}\displaystyle f(x) {/eq} considering the entire domain of the function...