SX IF X <1 Let F(X) = (^(X-2) IF XZ1 a, Find Limx→1¹ and lim x⇒ F(x) b. does LIM X→1 f(x) exist? C, Sketch the graph of f

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 2x2 + y2 −…

A:

Q: b) U2 X V3 = ||

A:

Q: Determine the cylinder's absolute max and absolute min given the function f(x, y) = 3x² + 2y² - 4y;…

A:

Q: 2 8 I Identify the factors of each expression to figure out the name of the Indian mathematician who…

A: Here, We have given some algebraic expressions now we have to find out their factors and then we…

Q: Where does the graph of sin x have a horizontal tangent line? Where does cos x have a value of zero?…

A: Given function is: y=sinx To find: Horizontal tangent line. and where does cosx have a value of…

Q: A 25-year-old woman burns 150 - 40t cal/hr while walking on her treadmill. Her caloric intake from…

A: calorie burned=187.5 calorie

Q: Find the (linear) equation of the tangent plane to the surface z=xexy at the point (7,0,7). Your…

A:

Q: 26-y 2. (Section 16.2) Consider [[ye² da dy -3 ²

A:

Q: 15 en vi - (-2) ₁² = (-3) - (2) ₁ - (-²), ₁² = V3 = = peform the indicated operations

A: Given query is to find the angle between V1 and V2.

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: Topic- Application of derivatives We are given, height of a ball launched in the air t seconds after…

Q: MULTIPLE CHOICE 1. Let f(x)=x-g(h(x)) where g(4) = 2, g'(4) = 3,h(3) = 4, and h' (3) = -2. Find ƒ'…

A:

Q: Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli…

A:

Q: The volume of a right circular cone of radius x and height y is given by 1 dy dx V = ²y. Suppose…

A:

Q: Suppose f(x,y)=x3y. At the point (1,2), in which direction does f have the maximum rate of change?…

A:

Q: slve the following I.V.P do +=y=y² Y= da B.C = (P.G.) 56). 1 3

A: Given differential equation:- dydx+12y=y3

Q: properties. 19. Both the function and the slope increase as x increases 20. The function increases…

A: To draw the graph of a function with given characteristics.

Q: Find the line that is tangent to the graph of the equation 2x^y+3xy^2-2x=-6 at the point (3,0).

A: We have to find the line tangent to the given equation.

Q: Find the solutions of the following quadratic equations by factoring: 7x²-14x=0 2 x² + 12x+27= 0 3…

A:

Q: Let F(x) = f(x5) and G(x) = (f(x))5 . You also know that a* = 5, ƒ(a) = 2, ƒ'(a) = 10, ƒ'(a³) = 6…

A:

Q: 5) Evaluate the limit; sin (3x) Tan (3x) a) lim. хэо b) lim X. Sinx X30 1- cos X fin (3001) тилев…

A: We can solve both the questions of question-5 in the below steps by finding the limit.

Q: Determine f + g, f − g, f · g, f/g, and give the domain of each  f(x)=x^2−1,g(x)=x+1/x.

A:

Q: 2) Let f(x) = 2x³+x². Compute [f(a+h)-f(x)]/h, and find f'(x) using only the definition of the…

A: We can solve as follows

Q: Find lim h(x), if it exists. (If an answer does not exist, enter DNE.) X→∞ (a) (b) (c) f(x) = 3x² +…

A:

Q: Use the method of Lagrange multipliers to find the point/s on the parabola y = 3x2 that is/are…

A: Let's find closest point to (0,3).

Q: The graph of the solution region for the system of inequalities is shown below. Locate all corners.…

A: we can find all the corner point of the graph .

Q: 10. Refer to the figure and find the volume generated by rotating the given region about the…

A:

Q: The following graph corresponds to f(x). If the graph does not appear, please reload the page. X y…

A: Graph of the function is given, We have to find the number of critical points, local maximum and…

Q: find dy/dx   y^y =x^x

A:

Q: Use the disk method or the shell method to find the volumes of the solids generated by revolving the…

A:

Q: 5. y = cosh[tanh(sinh(x))]

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Let f(x, y) = 3y2−2y3−3x2+6xy. Find all critical points of f and use the Second Derivatives Test to…

A:

Q: The function decreases and the slope increases as x increases. decreases as x increases. [Note: The…

A:

Q: Graph the feasible region for the follow system of inequalities by drawing a polygon around the…

A:

Q: 3. A man 5 feet tall walks at a rate of 4 ft/sec directly away from a street light which is 20 feet…

A: As per our answering guidelines we are allowed to solve only first complete question. I am solving…

Q: verify that the function. solution to the differential and find the y=c₁e-x + C₂ e 2x is a equation:…

A: Topic = Differential equation

Q: 3 a. Find an equation for the line perpendicular to the tangent to the curve y = x - 16x + 4 at the…

A:

Q: Consider the following. u = (3,9), v = (6, 2) (a) Find the projection of u onto v. 54 18 10' 10 (b)…

A:

Q: Suppose f is a one-to-one differentiable function and its inverse f^-1 is also differentiable.  a).…

A:

Q: Find the fundamental set of solutions of the DE y" + 4y + 4y = 0. Use the Wronskian or any other…

A: Given the DE is y''+4y'+4y=0.

Q: V. Identify the value/s of x for which the corresponding function evaluation is true. Show complete…

A: 1) f(x)=3x-4; f-1(x)=-2 2) g(x)=-5x+12; g(x)=57 3) h(x)=4x2+4x+3=0; h(x)=0.

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A:

Q: 12. Refer to the figure and find the volume V generated by rotating the given region about the…

A:

Q: EXERCISES Evaluate each of the following integrals. 43. S Do dz I + ar Q² by using the reciprocal…

A:

Q: Find the limit algebraically: √x - 11 lim 101 Mo 121)

A:

Q: Which function is the inverse of the function f (x) = x³ + 1 O g(x)=√x-1 O g(x) = 3x - 1 O g(x) = x³…

A:

Q: Evaluate the integral by interpreting it in terms of areas. L₁ (5+ √1-x²) dx

A:

Q: 5. Find the general solution of the DE y" – 4y' — 12y = sin(2t).

A:

Q: 11. Refer to the figure and find the volume generated by rotating the given region about the…

A:

Q: (1)x 2 0 -1 -6 -5 -3 -2 -1 0 t 1 2 3 4 5 6 Determine the generalized derivative of r(t) and plot it.…

A: Equation of a straight line is y-y1=y2-y1x2-x1(x-x1)when (x1,y1) , (x2,y2) are any two given…

Q: x² + 3x + 1 x² - 4 (c) / 2² (a) | dx x arctan x dx

A: