Q4(a)- If fE R(a)on [a, b, a < x < b and F(x) = S* f(t) dt] then F(x)is continuous on [a, b].

Q: Let f be a function such that f' is continuous on [a, b] Show that a

A:

Q: Define f : R2 → R by letting (y² – x)² (y4 + x²) f(x, y) = if (x, y) # (0, 0), and f(0,0) = 1. ||…

A: The given function is f:ℝ2→ℝ defined as: fx,y=y2-x2y4+x2if x,y≠0,01if x,y=0,0 Claim: The given…

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

A:

Q: Let ƒ : [a; b] → R be a continuous function and let F(x) = f(t)dt where x > a. (a) Show that if f is…

A:

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

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

Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Exercise 4: Suppose f is differentiable on (2,6) and continuous on [2,6. Suppose further that 1 < f'…

A: Given:f is differentiable on (2, 6) and continuous on [2, 6].

Q: Prove that if f is continuous, then f(t)(x-t) dt = f(u) du ) dt

A:

Q: What value of c makes the following function continuous at (0,0)? f(z, y) = C, x+ y³ +2, (x,y) +…

A:

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: The linear functional F: R^2[x] -&gt; R is defined by the formula F: p -&gt; ∫(from 1 to 0) p(t)dt.…

A: Step 1: Step 2: Step 3: Step 4:

Q: 10 1 If f is a continuous function and F'(x)=f(x) for all x € R, then fGx)dx=? LF(10) – F(2)] [FIS)-…

A: We have to find the integral

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.