1-cosx , x*0 is continuous at x=0 Find k so that (x) =; 4x2 Ik, x=0 A 1/2 в) 1/8 (с) 3/4 D) 2/5

Q: 1/x tan TC + x f(x)= .For what value of k, f (x) is k, continuous at x 0?

A: Introduction :We have given a function f(x) we have asked to calculate the value of k , if f(x) is…

Q: et [a, b] be a real interva b]→X is continuous, the is continuously differentia

A:

Q: (x2 -7 , 0b Is fdifferentiable at b?

A: Given that: f(x)=x2-7,       0<x≤b6/x   ,        x>b

Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x<πmx+b,      x≥π Since the function fx is continuous…

Q: Let f (x) = cos x – sin x for 0 0 and where is f (x) < 0?) A =

A:

Q: Express the limit as a definite integral on the given interval. lim > n- 00 eši . Δχ [0, 8] 5 + Xi i…

A: Given: limn→∞ ∑i=1nexi5+xi∆x,   0,8. To Show: Express the limit as a definite integral on the given…

Q: 12. Evaluate the triple integral xyz dxdydz for the following limits:  z from 0 to y, y from 0 to 4,…

A: according to our guidelines we can answer only  first question and rest can be reposted.

Q: If f isa differentiable function satisfying f(0) = 0 and f (0) = 2, then 1- cos( f (x)) lim x-0 A) 0…

A: The given limit is, limx→01-cos(f(x))x2. Note that, the given limit is of the form 00. Apply L…

Q: Let f (x) = cos x sin x for 0 0 and where is f (x) < 0?) A =

A:

Q: 2.6. Let ƒ be continuous on [0, a]. If x e [0, a], define fo(x) = f(x) and let %3D 1 fa+1(x) = -…

A: We will use the basic knowledge of integral calculus to answer this question. Note that we can only…

Q: f(x) = 1+x tan? r is f(x) uniformly continuous on [0, +o0)? Prove your result.

A: TheoremIf f:[0,∞) →R Be continuous on[0,∞) and limx→+∞ f(x)=0, f isuniformly continuous on…

Q: 3. Give the definition of a continuous function (at a point ao) of one variable. Find (if possible)…

A: The function is said to be continuous at x0 if limx→x0f(x)=f(x0) where both limx→x0f(x) and f(x0)…

Q: 5x sec Suppose m' is continuous at r = 0 and m'(x) if x > 0. log3 (2.x + 1) + cosh r If m" (0) = 0,…

A:

Q: 2. 지2 f f Š{(») = 6 , evaluate f(2sin6) Coso d@ is continuous and Sf(x)

A:

Q: Let f (x) = COS X sin x for 0 0 and where is f (x) < 0?) A =

A:

Q: Q1/ N Use the Trapezoidal rule to estimate the value of f(x) -2x sin'x in the interval x-0 to X-x…

A: A)f(x) = 2x sin2xfrom x = 0 to x = πwith n = 5Trapezoidal Rule∫ab f(x)dx = ∆x2 (f(xo) + 2f(x1) +…

Q: 2. Given the function f (x) = x2 + 2x – 3, calculate the area between the graph of f and the X axis…

A:

Q: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

A:

Q: Q1 (a) Sketch the graph of two continuous function g(x) = cos x and h(x) = on the same plane,…

A: Solution is here

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. Prove that h' is not differentiable at x = 0. .

A:

Q: (x²-x for x +0 If f(x) : and if fis continuous at x = 0, then k= 2x f(0) = k -1/2 O 1/2 O 1

A: f(x) = (x2 - x)/2x limx→0 x2-x2xlimx→0 x(x-1)2xlimx→0 x-12= -12

Q: [2x – 5] x if 0 3. - Determine if f is continuous or discontinuous at x = 0 and at x = 3. If di…

A:

Q: xy cos.x f(x, y) =+3y²

A:

Q: Let y =[F(sin(3x))] 5 for some differentiable function F. Determine Y at x = 0 dx given that F(0) =…

A: Given function is y=[F(sin(3x))]5  and F(0)=3 ,F'(0)=1/27

Q: No. 2: X and Y are jointly continuous with joint pdf (CL if 0 Sxs 2,0 Sys2 f(x,y) = {k(3x² + y³) 0,…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: S(1+ x)? – 1, x 0 Find out whether g(x) is differentiable at x = 0 using the differentiability…

A:

Q: ( g(x) + a, xsO 13-b cos x, x>0 Let f(x) be given by the function f(x) = where a and b are constants…

A:

Q: Sx²-x²+1 1-sin x if x20 ) Let f(x) be defined as f(x)={* 0>x Is f(x) differentiable at x = 0? a) Is…

A:

Q: Q: Find a continuous function f (x) satisfying x*– 4x'<f(x)<2x -x' for all x e [0,2] such that the…

A: In this question we have given a relation and with the help of this one we have to find the function…

Q: Suppose that g(x) is a continuous function, g(0) = 2, g(1/2) = 1 and g(x)dx = 3. Evaluate the…

A:

Q: Set cos , x +0 f(x) = x = 0. Note that f is not continuous at 0. Nevertheless, F(x) = | f(t)dt is…

A: Second Fundamental Theorem of Calculus: If F is differentiable on a,b  and the derivative F'=f is…

Q: x² Find the area under the curve f(x) = from x = 2 to x = 6 using the limit of the 5 Riemann sum

A: The formula for the Reimann sum is given by , where a and b are the endpoints of the function, f(x)…

Q: Suppose f is a differentiable function with f(7)=1 and f '(1)=- Let y= f(x)·tan x+e* •cos x . Then…

A:

Q: Using the definition of integral12. x^2 dx as a limit of a sum of rectangles, compute integral12.…

A: Given ∫12x2dx

Q: 2? sin ? a +0 x = 0 Let f(x) = (c) Show that f'is not continuous at x = 0.

A:

Q: [ 2 sin(;) 15. Given that f(x) =- ki, is a continuous function at z = 0, the value of k is x = 0 B !…

A: A function f(x) is continuous at x=a, if right hand limit = left hand limit = function value at x=a…

Q: what is wrong with the following equation? A. f(?) = 6 sec(?) isnt continuous at ? = ?⁄3, therefore…

A:

Q: The area between the curves y = 3 cos (z) + 3 and y = -3 cos (r) on the interval (0, n) is: -T+6/3…

A: We need to determine the area enclosed by both curves. If fx&gt;g(x) in an interval a, b, then the…

Q: B/ For what value of a is fa continuous at every x? x2-1, x<3 fo 2ах, x2 3

A:

Q: x-1 for x 1 x -1 show that flx) is continuous at x = 1 !3! for x 1,

A:

Q: Find the value of parameter A that makes f(x) continuous for all real numbers. S(x) = x² +4,x1 Write…

A:

Q: Show that, dF(x) (i) if F is absolutely continuous, then exists almost everywhere. dx (ii) a…

A:

Q: a non zero valie for the constant k that makes the fmction ww m tan(kx) x< 0 f(x) = 3x + 2k?, x 20…

A: To find a non zero value for the constant k that makes the function…

Q: 12. Suppose that X and Y have a continuous joint distri- bution for which the joint p.d.f. is as…

A:

Q: (c) Use only the e – 8 definition of continuous functions to directly prove f(x) = x² sin(x) is…

A: In the given question we have to solve the part c of the given question. In this part we have to…

Q: 2″ Given f(x) = xr-¹e-λx, x > 0, r, λ > 0. Γ(r) 2. Evaluate etx f(x) dx. HINT: Express f etx f(x) dx…

A:

Q: sin(bx) x0. Find a value of b such that f is continuous, or explain why no such value exists.

A: Given, f(x)=sin(bx)xx&lt;0exp(x+5)x≥0