Q3) Detemmine the points of discontinuty, if any, of the following functions : x² +3 (a) x +x+1 4x +3x+5 (b) x - 2x +4 x +x +1 (b) x - 3x 1 Jxt-16, x 2 16. x=2 (d) f(x) = 16, х %3D2

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: What is the value of a such that the function y = 2x4 - ax² + 3 has twin global minima at x = -3 05…

A:

Q: 11. Differentiate the function (use chain rule): y = x²(x-1)³(2x-5)² ;

A:

Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

A:

Q: Are the f-llowing functions Continual s OFC メーE X-2 スト=メ 1P 2) FCX)s X- S X +7 at XE-1 X5qXs (xフゴ

A:

Q: 2. Identify the iterative function f(x) = x3 – 9x2 – 6 if initial approximation x, = 2.25

A:

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

A:

Q: Suppose (2, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: We need to choose correct option.

Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

A: Given  f(x) = x8-5x4+5x3-1 We have to find the end behavior of the function.

Q: 7. Consider the function *+1 if r< 2 f(x) = 3-1 if z 2 2 (a) Show that ƒ has no fixed point.

A:

Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: Find the critical numbers of the function f(x)=f(x)=-12x^5-75x^4+40x^3-1 and classify them. Round…

A: Consider the given function f(x) = -12x^5-75x^4+40x^3-1

Q: The critical points of the function f(x) 36z2 - 2x occur at 2- 0, r +4.00 0, z +2.40 %3D I0, z -…

A: We have to find the critical points of the function f(x)=36x2-2x4.

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Points at which fx = fy = 0 are called critical points.

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

A:

Q: Vhat is the largest output value of the function z = 2x + 2y that can be obtained by plugging in…

A: In this question, the value of the function is checked at the corner point. The maximum value of the…

Q: How many critical points does the function f(x)=∣∣x3−12x∣∣ have?

A:

Q: Indicate all critical points of the function f(x)=∣∣x2−5∣∣.

A:

Q: 1. f(x) = x² – 4x + 1 at point (0,1) 2. f(x) = x³ + 2 at point (1,3) 3. f(x) = 2x* + 3x³ – 2x + 7 at…

A: Given : The functions and the points.

Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

A:

Q: 4.x +1 1 with f'(x) = 1/ 56x2 - 156x + 115 14x – 19 - - 3. Let f(r) = and f"(x) 4 %3D 3 5 Vr2 – 3x +…

A: To find the points on which it is concave up or concave down

Q: Find the critical numbers of the function f(x) = 12x5 Round your answers to three decimal places.…

A: the given function is fx=12x5-45x4-40x3+2

Q: f(x,y) = y4 −2y2x−x2 +4x From the given function above, find all of its relative extremum points…

A: fwe have to find all of its relative extremum points and saddle points.

Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

A:

Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

A:

Q: Q.4. locate the critical points of the function f(x) = x²(x-1)³ and identify critical points which…

A:

Q: The rate at which the total average number of COVID cases is increasing at x=10 tents and dxdt=1…

A:

Q: A goldsmith finds that the demand for gold is governed by p(x) = –x² + nx, where z is in (troy)…

A:

Q: Determine all the critical points for the function y = Vx² (2t- 1)

A: Given function is in two variables x and t For critical points we calculate Partial derivatives…

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case,…

A:

Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: Let F(x) = [ (3t2-3)dt then F"(1) is equal to:

A: The Fundamental Theorem of Calculus : If f is a function that is continuous on an open interval I,…

Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

Q: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the same set of…

A: To Determine: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the…

Q: 2. Integrate the function (x+2/x)ax using multiple-application trapezoidal rule with n= 3

A: Trapezoidal Rule: ∫abf(x) dx≈∆x2(f(x0)+2f(x1)+ ... +2f(xn-1)+2f(xn))where ∆x=b-an

Q: Use the First Derivative Test to classify each critical point of f(x) = x^4 − 8x^2 + 3 as a local…

A:

Q: Compute f(c+h)−f(c) at the indicated point. f(x)=6x2​; c=4

A: Given : Function : f(x) = 6x2   To find : f(c+h)−f(c) at c = 4.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4,…

A:

Q: The function f(x) = 2x° – 33x + 180x 2 has two critical points. The smaller one is x = and the…

A: We have to find

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

A:

Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

A:

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.