) Given the piecewise defined function f(x) = {10x b) lim f(x) (10x-5,x<3 3x², x ≥ 3 c) lim f(x) a) lim f(x) e) Is f(x) a continuous function? Explain why, or why not. find d) f (3)

Q: Which of the following is/are functions? Select ALL the CORRECT answers. O Input (x) 2 Output (y) 12…

A: To be found - Functions from given options

Q: 2. (6x+y²) dx + (2xy-3y²) dy

A:

Q: The graphs of y = f(x) (solid) and y = g(x) (dashed) are shown. The two graphs intersect at (15,…

A: Ques 1 ∫015gx-fxdx This integration result in area of REGION 1. Hence answer is 11.

Q: Find an arc length parametrization of r(t)=

A: Given, r(t)= &lt;6t2,t3&gt; Formula : Length of parameterization: L= ∫0t|r'(t)| dt

Q: 4. Find the exact value (in exact form) of sin

A: cos(2x) = 1-2sin2(x)

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: y = ((x³- 2)/(x³ + 1))³ dy/dx =3( x³-2/ x³ +1 )² × [ ( x³ + 1)3x² - (x³ - 2) .3x²/ (x³ +1)² ] dy/dx…

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: The function is given by y = x3-23x2+4 To determine: The derivative of the function.

Q: (b) Express sin(cos x) in terms of x only.

A:

Q: K Given that g'(x)=6x²-7 and g(6) = 40, find g(x). g(x) =

A:

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

A: Understanding of function and how to calculate its derivative is required in order to solve this…

Q: f(x) = 0, COS . x≤0 X>0 Complete parts (a) through (c)

A: a. Answer : B : limit does not exist   b.

Q: How much of a 7% HCl acid solution needs to be mixed with how much of a 15% HCl acid solution so…

A: Solution

Q: II. Find the equation of the normal line to the curves at the point of tangency, if given. 1. y…

A: Recall: The slope of tangent line to the curve y is, mT=y'x0,y0 The equation of the normal line is,…

Q: y=3e^x + 4/∛x *differentiate the function.

A: Topic:- derivatives

Q: Where did the -1/3 come from? Is it because the 3 is the nth root and the 1 is the one inside the…

A:

Q: The graph below is the function f(x) 3 2 OF -5-4-3-2-1 Find lim 24-1 Find lim 24-1¹ Olim f(x) 2411…

A: As x tends to Right side f(x) tends to -1 , therefore limx→-1-f(x)=-1

Q: tal derivatives of the following function dz: z = 4x² - 3xy + 2y², where x = (CW P.193, Exercise…

A:

Q: Make an ORIGINAL EXAMPLE OF "Variable Separable" A) GIVEN B) SOLUTION C) ANSWER D) WITH EXPLANATION

A: Given expression, Solve 1+x2dydx=1+y2

Q: 1. Use deductive reasoning to show that the following procedure produces a number that is three…

A: Deduction or deductive reasoning begins with the general statement/hypothesis and investigates the…

Q: The hyperbolic tangent and secant are defined as sinh tanha cosh a 1 cosh a sech a Find the…

A:

Q: Determining the Maximum and Minimum Values of Quadratic Functions A rocket is launched in the air.…

A: This question can be solved using the concept of maxima and minima

Q: (-7)=|

A: Topic:- derivatives

Q: Determine whether the function is even, odd, or neither f(x)=tan(x) cos(x)

A:

Q: K|3 0 sin(3x) cos(x) Integrate By Parts

A: Solved using the given formula

Q: At what points is the function y= X+7 2 x² - - 8x+7 continuous? Describe the set of x-values where…

A:

Q: Consider the integral fa¹ In(a) Applying the integration by parts technique, let U = In(x) dv = x4…

A: This question is based on Integration by parts technique.

Q: The graph below is the function f(x) 4 34 2 01 -5 -4 -3 -2 -1 Find lim I→-1 Find lim z→-1+ 2 A Find…

A:

Q: Use this table about differentiable functions f and g to answer the following. x f(x) | f'(x) g(x)…

A:

Q: Determine whether the points lie on a straight line. (a) A(2, 6, 1), B(3, 10, -1), C(1, 4, 2) O Yes,…

A:

Q: . Find equations of the tangent lines to the curve x-1 x+1 that are parallel to the line x - 2y = 2.…

A:

Q: Evaluate the indefinite integral: dx S x In 7x +C

A: Let ln7x = t

Q: (cos x-cosy-cotx) dx-sinx.

A: Topic:- differential equations

Q: 3. f(t) = 3t - t², (0,0) 4. f(x) = 3-5x, (-1,8) 5. g(x)=x²-9, (2,-5)

A:

Q: 1. y=x²(x-1) at the point (2,8).

A: find slope Given point ( 2 , 8 ) for x = 2

Q: Let f(t) = et+3-7√5 + 3t-14. Find the first derivative: ƒ'(t) = Find the second derivative: f"(t) =…

A:

Q: A manufacturer produces bolts of a fabric with a fixed width. A quantity qq of this fabric (measured…

A: I am attaching image so that you understand each and every step.

Q: Consider the function f(x) = 4 sin(x) cos(x) + 6 csc(x). Evaluate its derivative at the point x =…

A: Product rule of derivative is used.

Q: Evaluate the integral. (Use C for the constant of integration.) in² (7) dt

A:

Q: дz Use implicit differentiation to find and 3, Əy дz ?х

A:

Q: G(r)=3r^3/2 + r^5/2 /r  *differentiate the function How do I approach problems like this? Like…

A:

Q: Derive the following functions 2-3x 5 50. y=- 6 3+x 52. y=: 54. y=- Sx²

A: 50. y=2-3x5

Q: b) H(x) = (3 sin x + 5 cos x) e²

A: Given query is to find the derivative of the function.

Q: Evaluate f cos³ x(sin x) dx O (sin x) [-sin² x] + C O (sin x)[-sin x] + C O(sin x)2/5 + sin x + C…

A:

Q: Find the limit times x-6- (x-6) 2

A: Given problem:- limx→6-1x-62

Q: LET 9 (3)=4₁ g (3)=-1 FIND H (3) For H(X) = xg(x) 5x-6 FUNCTION

A: solution is given below..

Q: Evaluate the integral. (Use C for the constant of integration.) [√ cos(6) sin³ (8) de

A:

Q: Find the intersection of the line / and the plane T. 1:ř=(4,-1,4)+t(5,-2,3) T: 2x+5y+z+2=0

A: Given line, r=(4i-j+4k)+t(5i-2j+3k)               (1)And plane ,2x+5y+z+2=0…

Q: 1. Given the function y = x4-2x²: a. Determine the maximum point/s. a. (0,0) O b. (-1,-1) O c.…

A: In order to check maxima and minima we have to differentiate given function twice and check for sign…

Q: Find the solution of the IVP Then, evaluate y(1.063). x²y" = (y')², y(1) = 0, y′(1) = −1

A: Given 1. x2y"=y'2 2. y1=0 3. y'1=-1

Q: here is the function f(x) below discontinuous 4, (x)=x²-5, x + 3, if x 1

A: Given query is to find where is function discontinuous.