This fact together with the equalityimply thata.n for any integers.SinceSimilarly, we havefor any nonzero integer.And we can showfor any integer(is non-zero) (for exampleHence we have proved thatfor any rational number.Consider the function. It is continuous and it is zero at all ...
is a continuous function.
解析 $$let G_{1}(iv_{eh}\int f^{\prime}(2x+1)dx=? \\ 2x+1=5 \\ 2dx=dt \\ dx= \frac{dt}{2} \\ > \intf^{\prime} (t)\frac{dt}{2}= \frac{1}{2}\int f^{\prime}(t)dt \\ = \frac{1}{2}f(t)+c $$ $$ = \frac{1}{2}f(2x+1)+c $$optionD. ...
Is there a quick way to see that this function is continuous? Let $f,g: [0,1] \to X$ be a continuous function ($[0,1]$ has the subspace topology), where $X$ is an arbitrary topological space. Define $h: [0,1] \to X: t \mapsto \begin{cases}f(2t) \quad0 \leq t \le...
Answer to: If f(x) is a continuous function satisfying f(x)f(1/x) = 3f(x) + 4f(1/x) and f(1) is greater than 0 find \displaystyle \lim_{x \to 1}...
Given y is a continuous function of x on the interval a≤ x ≤ b, where x= f(t) and y=g(t).Also f(t_1)=a, f(t_2)=b and both g and f' are continuous on [t_1,t_2].Differentiating both sides of x=f(t) with respect to t, we get,(dx)(dt)=f'(t)⇒ dx=f'(...
Step by step video & image solution for If f(x) is a continuous function in [2,3] which takes only irrational values for all x in[2,3] and f(2.5)=sqrt(5) ,then f(2.8)= by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams.Updated on:21/07/2023...
If f'(x)=g(x) and g is a continuous function for all real values of x, then \int_{0}^{2}g(3x)\d x is ( ) A. 13f(6)-13f(0) B. f(2)-f(0) C. f(6)-f(0) D. 13f(0)-13f(6) 相关知识点: 试题来源: 解析 A Let u=3x; \d u=3\d x or \dfrac{\d u}{3}...
iff(x)is a continuous function on[a,b], then∫abf(x)dxis a number: True or False Integrals: The integral of a real-valued functiony=f(x)on the closed interval[a,b]can be seen as the area delimited by thex-axis, the linesx=aandx=band...
Answer to: a- A continuous function is always integrable. - True - False b- A differentiable function is always continuous. - True - False...