Find the area bounded by the following:  f(x) = 2x2 + 10 g(x) = 4x + 16 x = - 2 x = 5

Q: Derive: y = (5x-2)(2x + 3)-²

A:

Q: x 0 Can also be displayed as: f(x) = [x - 1 when x < 0, 1 when x = = 0, x² 1 when x ≥ 0] For this…

A: The given function,     fx=x-1,x&lt;01,x=0x2-1,x&gt;0

Q: B = {x ER: x is a counting number} = {1,2,3,...} C = {x ER: x = 2n + 1 where n is a nonnegative…

A:

Q: 7. 1 x lnx dx 8. f(x + 1)(2x - 1) dx

A: 7.∫1x lnxdx = ∫1 lnx. 1xdxLet, lnx= y ⇒1xdx = dySubstitute the corresponding values in the…

Q: [Select] the derivative of y? y = x⁹e²x+1 18. Which rule is applicable when solving for A.…

A:

Q: 7. √16-e2x e* -dx

A: We can solve the integration as below.

Q: Let Use the limit definition of the derivative to calculate the derivative of f: f'(x) = Use the…

A: Given: f(x)=3x3-6x-4

Q: Read, analyze and solve for the following. Express your answers as decimals rounded off to two…

A:

Q: R is the region bounded by the functions f(x) = 3x² + 27x + 54 and g(x) = -3²-22-27. Find the area A…

A:

Q: 3. Test the following series for being convergent or divergent: (2) Σ < (3n)! n!(+1)!(+2)! (c) Σ…

A:

Q: Direction: Evaluate the following Definite Integrals Show a complete solution and annotate each…

A:

Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population…

A:

Q: C. length x, width = D. length = 2x, width - [Select] da = 24 = 24 V What is the appropriate…

A:

Q: [Select] A. f(x) = 3x² + 2 B. f(x) = 3x² +4 C. f(x) = 4x³ D. f(x) = 3x4 [Select] A. 6 B. 5 C. 3 D. 2…

A: topic- functions and limits

Q: fxe-*dx= 303 blow Sie f sin (In y)dy =

A: Integration by parts : ∫u·v dx = u·∫v dx - ∫ddxu·∫v dx dx

Q: Which statement is TRUE about trigonometric functions? O a. The derivative of sin x, cos x and tan x…

A: The answer with explanation is given below:

Q: Find the second derivative of f(x) = 9 sin (2x). Enclose arguments of functions in parentheses. For…

A: On solving this we will get

Q: e Sc (4x + 3√y) c Evaluate figure. ds where C is given in the accompanying CH 1- (0,0) y=x O (1,1) X…

A:

Q: Enter an exact numeric answer. To enter ∞ in your answer field, ● When you are in text entry mode…

A:

Q: 10. X dx

A:

Q: (a) An archaeological artifact is found to have 45% of its original carbon-14. How old is the…

A: Decay and half life

Q: The derivative of f(x) with respect to x is the function f'(x) and defined as f(x+h)-f(z) f' (z) =…

A: topic- derivative of a function

Q: 1 f(x) = (2x³ + 6) ³

A:

Q: f(x)= (7x¹-5x-2)

A:

Q: 19. x'dx √√5x² +4 -S

A:

Q: 149. Determine the real number a such that vectors a = 2i +3j and b=9i+aj are orthogonal.

A:

Q: For the function gox) graphed here, find the following limits or explain why they do not Im gox) e.…

A: Given,

Q: If f(x) = 5x (sin x + cos x), what is f'(x)? ○ 5 (sin(x) + cos(x)) + 5x (cos(x) = sin(x)) O No…

A:

Q: 13. (2x³ +9x) dx ²+3)(x² − 2x+3)

A: Given

Q: Which equation shows the correct derivative of the equation y = 2x² + 14x + 5? Oy = lim- 4th + 2h² +…

A: On solving this we will get that

Q: y=x², y = 1, y =9 y=9, first quadrant

A:

Q: 1. Let S be the solid of integration of the ff. integral Q. Sketch S and label its boundaries. 16-y²…

A: Q=∫-44∫016-y2∫0y+6y2z dxdzdyS is the solid of integration of the integral Q.Sketch S and label its…

Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

A:

Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…

Q: 1/A) Replace the polar equation by equivalent Cartesian equation r2cose + 2sino

A:

Q: Consider the following families of sets indexed by the set of natural numbers. i which among these…

A:

Q: Evaluate the indefinite integral Sxe-xdx O-X-1 ex O X-1 ex O -x+1 e-x O-x-1 e-x -X =+C + C = + C - +…

A:

Q: (x - 2y - 1) dy = (2x - 4y - 5) dx

A: Solution:x-2y-1dy=2x-4y-5dxdydx=2x-4y-5x-2y-1dydx=2x-2y-1-52+1x-2y-1dydx=2x-2y-1-32x-2y-1let,x-2y-1=…

Q: A piecewise function is defined as f(t) = {4,5 t 0 ≤t <3 t≥3 i. Sketch the graph of f(t). ii.…

A:

Q: 3. Let B=(2,4,6,8,10), C=(4,8, 10), and D= (xxis even). Answer the following questions. Explain (a)…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: 6. ၂ 3z+1 -4) -dz

A: ∫3z+1(z2-4)2dzExpand:=∫3z(z2-4)2+1(z2-4)2dz=3∫z(z2-4)2dz+∫1(z2-4)2dzNow solving…

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: Prove using the properties of set operations: a. If A and B are sets then [(A - B)c n A] C B

A:

Q: - a. Find the derivative of 3y – 2xy² = sin x + cot y b. Find the derivative of 2y x(3³) – In(²/²) =…

A:

Q: mathematically

A: We will solve the problem

Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

A: topic- application of derivatives

Q: Question Define R as the region bounded by the functions f(x) = e and g(x) = e between x = 0 and x =…

A:

Q: As shown in the required readings or videos solve the Logistic Differential Equation below for an…

A:

Q: Use implicit differentiation to find an equation of the tangent line to the ellipse at the given po…

A:

Q: 4. f(x)=

A: The given function is: fx=5x2x+3   As we know that; The Power Law: ddxxn=nxn-1 The Quotient rule:…