Suppose f and g are continuous on [a, b] and f f(x) dx = S% 8(x) dr. Prove that there is cE [a, b] such that f(c) = g(c).

Q: xy' - y = = x tan Y 18

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Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: Let f:A-B and X,Y be subsets of B. Then f-¹(XnY) = f'(X) nf-¹(Y). True False

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Q: f:R-R is differentiable on R. There exist monotonic increasing functions g(x) and h(x) such that…

A: Definition continuity of a function f(x). A function f is continuous at x=a when: (i)  f(a) is…

Q: True or Fal se ? Continuous on Cagb], then %3D

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Q: Show that the function f (z) = Z is continuous at the point z=0 but not differentiable at z=0.

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Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

Q: the function f is not differentiable at x=0.

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Q: (6) Are all continuous functions on ID differentiable on D?

A: we have to identify the given statement is true or not

Q: Prove that the derivativeo P(zx tJ's 4(2Xbjusiy Pirst Princiele 4(2X+)by jusing first Princiele…

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Q: Please

A: Given function is

Q: Determine whether the statement is true or false. '8 If f'is continuous on [7, 8], then f '(v) dv =…

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Q: If f (s Continuous then on -fex) True or felse?

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Q: V.EVALUATION: Given the following scores: 5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65. Find: 1. Qi…

A: The given data is already in ascending order: 5,7,12,14,15,22,25,30,36,42,53,65 Q1=(n+1)4thterm…

Q: Let f(x) — sin(nx) n³ n=1 Show that f is differentiable on R and that f' is continuous on R.

A: Within its interval of convergence, the derivative of a power series is the sum of derivatives of…

Q: Find the continuous lest squares approximation of degree 2 for f(x) = cos(xx) on [0,1]. %3D

A: Let P2(x)=a0+a1x+a2x2 is the continuous least square approximation of degree 2 for the function…

Q: 10 If f is a continuous function and F(x)=f(x) for all x € R, then x)dx=? A © FS) - F)] B ©2[F(5) –…

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Q: Prove that f(2) = z/(z* + 1) is continuous at all points inside and on the unit circle Iz] = 1…

A: we need to find those points where the denominator ( z^4+1) equals to 0

Q: Show that the function f defined on [0, 1] by the conditions 1 f(x)=2rx when 7=1, 2, 3,...... És…

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Q: If f is a continuous function on [a, b], ƒ is differentiable on (a, b), and if both f(a) and f(b)…

A: This question is based on Rolle's theorem which is explained in step 2.

Q: Show that a function f : R2-R defined by f(x,y)= x3- y3 / x2+ y2, if (x,y) is not equal to (0,0)…

A: What is Continuous Function: A function is referred to be continuous at a certain point in its…

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: show that the inverse of arotation matrix is transpose,which is also arotation matrix, and it is…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.