|x + 2, x> 0 讨论函数f(x) = 在x=0的连续性. х — 2, х <0 -

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

A:

Q: 21. f(x) = In (5-3x²)' J6x² + 21. f(x)= In| (5-3x V6x? + 8х —12 1+5t 22. f(t)= In(t)

A: As per our guidelines, I can answer maximum one question. Since you have asked for multiple…

Q: e^x=3-2x

A: Given; ex=3-2x,(0,1)

Q: If f(0) = 0 and f"(x) exists for all x>0, then show that %3D f(x) f'(x) xf"(5), 0 < § < x. Also…

A: Let's find.

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

A:

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: ,u(x) -f(x) - I(x) 1.5- 2 3 4 In the figure, is f(x) squeezed by u(x) and 1(x) |? 1. at x = 3? |? 2.…

A:

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: Show that f(x) = 0(\x – #o|*) and g(x) f • g(x) = o(\x – xol*+i). o(lx – xo|2) imply -

A:

Q: The range of F in F(x) = 2 sin x; - < x< 2 T is: %3D -2SF(x)SO F(x)S2 ) -2SF(x)S2 O O

A: Given:- F(x)=2 sinx  ,-π/2 &lt;x &lt;2π To find:- Range of F(x)

Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

A:

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: 1. f(x) = x² +x – 1 for all values of x -

A:

Q: -2 Find the interval(s) where f(x) =- 64-x2 is continuous.

A:

Q: If f"(x) = V - cos(x). f'(0) = 2, and f(0) = 0, find f(x). %3D

A:

Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x^2+2x−3, what is h′(x)?

A: Given,          hx=fxgx. And fx=-cosx  and  gx=4x2+2x-3.

Q: The interval on which f(x) = 3 – 2x – 12x² – x³ is | - concave down is: O (-4, 0) O (-∞, 4) O (4,…

A:

Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

A:

Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

A:

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx2 + 8x x3 - cx if x < 5…

A:

Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

A:

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: Find (f-)'(a). f(x) = 4 + x2 + tan(Tx/2), -1 < x < 1, a = 4 %3D (F-1)'(a) =

A:

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: 81 xf(x²) dx. 6. If f is continuous and f(x) dx = 4, find

A:

Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

A:

Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: f (x) = x' - 4x + 2x – 3 %3D as x → -o0 f (x) → ∞ as x -0o f (x) → -0 as x →+of (x) as x +oo f(x) →…

A: topic - polynomials option - B

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

A:

Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x2+2x−3, what is h′(x)?

A: If f(x)=−cos(x) and g(x)=4x2+2x−3, what is h′(x)?

Q: f(x) = In(1 + x5) %3D f(x) = Σ n = 1

A:

Q: Suppose f'(x) = c for all x, where c is a constant. Show that, for some constant d, f(x) = cx + d.

A: suppose f'(x) =c for all x, where c is constant .Show that for some constant d, f(x)=cx+d

Q: Show that the function is differentiable at x=0 and find f'(0). f(x) = x2sin(1/x), if x is not…

A:

Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

A:

Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: Prove that f (x) = x2 takes on the value 0.5 in the interval [0, 1].

A: Here given

Q: The function f(x) = x + 1/x is 2p O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1,…

A:

Q: Find the absolute extrema of f(x) = −x^(2) + 3x on the interval [0,3] .

A:

Q: The interval on which f(x) = VI-x is decreasing where x€ [-1.1] is

A: Given function f(x)=1−x2   on  [−1,1]

Q: If f(x) = sin (x² – 4), what is f'(x) ? %3D 2z o f'(x) = V1-(2²-4)² f'(x) = - V1-(2² 4)² o f'(#) =…

A: Given Data: Function: ffx=sin-1x2-4 The derivative of the sine inverse function is, ddxsin-1x=11-x2…

Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5].

A: There are more than one question. We will solve the first one. Given, f(x)=x-[ln(x)]x, we need to…

Q: 3 - x, x<2 Q.No.15: Is f(x) = {+2 x22 continuous at every x € R. x+1 xs1 -.

A: Continuity of a function.

Q: 1+x Ex(11):-(H.W) If f(x)= 1-x f(x)-f(y)x-y 1+ f(x)· f(y) 1+ xy Show that

A:

Q: Find the interval(s) on which f(x) = 2x^3-3x^2-12x+1 is concave up.

A: Given : fx = 2x3 - 3x2 - 12x + 1

Q: Let f(x)=1x−2 ; for what values of x , f(x) will be discontinuous?

A:

Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

A: