1. Find the area under the curve y = 9- a2 over the interval[0, 3] using right end point approximation.

Q: (cos x - sinx +1) sin x cos x dx

A: You can solve this question by substitution method.

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: Circles and parabola are functions A. True B. False

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Q: Calculating Mass from Radial Density. Mass-Density Formula of a Two-Dimensional Circular Object. Giv...

A: Given: m=∫0r2πxρxdx  ...(1) And ρx=6x ; x=6   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 A...

Q: general function M(x, y) or N(x, y) so that equation is exact.

A: We will find the function (general). 

Q: 1 + 20 f(x) , g(x) h(x) The partial fraction decomposition of - + 3x2 can be written in the form of ...

A: Given that: x2+20x3+3x2

Q: 1.d) * when x = 0; y" e* + (y') = 5 True O False

A:

Q: y'dx-(xy + y* kty = 0 1. Let the substitution v=2; y= vx; dy = vdx+ xdv

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Q: Finding the length of a curve. Arc length for y = f(x). Let f(z) be a smooth function over the inter...

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Q: Use differentials to approximate the change in cost corresponding to an increase in sales (or produc...

A: Solution ) c = 0.075x2 + 6x + 2  with dx = 1  differentiate with respect to x  dc/dx = 0.075 × 2 x +...

Q: Agree. Disagree 1. Is it correct to say that we can only get an estimate of a limit? Why do You say ...

A:

Q: y = C,e²x cos(3x) + C2e2x sin(3x)

A: y=c1e2xcos3x+c2e2xsin3x  differentiate with respect to x dydx=C1(e2x3(-sin3x)+2e2xcos3x)+C2(e2x3cos3...

Q: The weekly cost for a small confectioner to produce g chocolate bars is C(q) = 1700 + 0.12q + 0.001g...

A:

Q: 14х10+8 еx F (x : 4 x' + 13

A: Given: fx=14x10+8ex4x+13

Q: Find the focus of the parabola 4x +24 =8y-y².

A: Given: - The parabola is, 4x+24=8y-y2 To find: - The focus of the given parabola.

Q: (I-) = 2- VT-I (b) i) Compute lim- ii) Hence prove the limit in i) above by -ố definition. 2

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Q: Solve the homogenous equation. 2. x*dy+(2.xy– y² kdx = Let the substitution v=: ²; y=x; dy=vdx+ xdv ...

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Q: 3sin4t dt 2. 5(1- 3cos21)

A: We have to find integral

Q: d the area (sq. units) covered by the line 2y = x + 6 from x1 = -8 to x2 = 0.

A: Given query is to find the area bounded by the curve.

Q: On the graph of f(x) = sec x and the interval [0, 27), for what value of x does f(x) = –1? Choose al...

A: We have to find out 

Q: x- 1 (i) y = () y = Vx(Vx+1) x + 1

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = x – x^2 and y=0 about th...

A: Given query is to find the volume of the solid generated. First we will find the intersection points...

Q: Below is the graph of y = x +5. 20- 15 10- -4 -3 -2 -1 0 1 The area bounded by y = x +5 and the raxi...

A: Given problem:- Find The area bounded by y= x2 +5 and the x-axis from  x=-3 to x = -1

Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = |F(z – 3i)| wh...

A:

Q: Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly int...

A: Given:The average score in percentage is given by:

Q: Find an equation of the line tangent to the graph of G(x) = 7 e -5x at the point (0,7). The equation...

A:

Q: x^2y=4+Cy Eliminate Arbitrary Constant

A: Here we will eliminate arbitrary constant,  

Q: Solve using homogeneous differential equation y'dx- (xy + y° kty = 0 Let the substitution y=? 2; y=v...

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Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if , 2. The function f(x, y)...

A: Topic:- calculus

Q: By using substitution method, evaluate: (a) dx (e3x+x3)3 (In x) dx (b) 4x

A: To evaluate the integral.

Q: Which of the following is not true? (A) - |f(x) dx- J8 (x) dx B) 8 (x) dx C) (x)dx=k (D) O fas(3))dx...

A: some properties of the integration are given, we have to find the not true statement.

Q: Beth is filling a small backyard pool with a garden 647. hose. The pool holds 30 gallons of water. A...

A:

Q: Evaluate the following Integrals: 1. 6x² sin x³ dx

A: NOTE: As per our guidelines, I have solved the first problem in the picture.

Q: 10 – 2x6 dx

A:

Q: 4. Solve the homogeneous differential dy equation dx + 9xe x .

A: Solution: Given data, dy/dx = 9xey/x +y/x Multiply by differential dx dy = (9xey/x +y/x)dx Divide by...

Q: Expand the expression. If possible, write your answer without exponents. 4. X, - 5 log 5 3+x² x-5 lo...

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Q: x(/x+y) +у) — 8 — ху

A:

Q: Finding the length of a curve. Arc length for y = f(x). Let f(1) be a smooth function over the inter...

A: The given function f(x)=253x32-8 over the interval 3,5

Q: Suppose C(t) is the cost, in thousands of dollars, of producing t tons of white paper. If C'(10) = 3...

A: suppose c(t) is the cost in thousands ot dollars ,ot producing t tons of white paperIf            C'...

Q: 1. y'dx-(xy + y* \dy = 0 Let the substitution y=2; y= vx; dy=vdx+xdv

A:

Q: të the area covered by the curv om xi X2

A: Given query is to find the area bounded by the curve from x= -1 to x = 1.

Q: On the graph of f(x) = cot x and the interval 2T, 47), for what value of x does the graph cross the ...

A: Follow the procedure given below.

Q: 3. Solve the differential equation by variable separable method (1+ y") (3a² + 6) dy 9- dr 13 + 6r

A: dydx=91+y23x2+6x3+6x  

Q: h" (t) = sec? t – Vt, h(0) = -3, and h'(0) = 3. %3D

A:

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic ...

A: We will find the T2(x) and T3(x) for the given function.Below find the solution in the image.

Q: Determine which of the following sentence are propositions and indicate their truth values. 3 + 4= ...

A: This is a problem of mathematical logic chapter. As per the definition of the proposition the senten...

Q: ()- 2y on [–10, 15]. Determine the absolute extrema of f (y) = sin

A: Here we have to find the absolute extrema.

Q: Center of Mass: Thin plate (region in the plane). Suppose Ris the region bounded by the graph of f(z...

A: We need to find center of mass.

Q: 1. Find the order and degree of the differential equation: dy +5 dx 4 14 sin x. dxº

A: Given- d9ydx9+5dydx4=14sinx To find- order and degree of given differential equation

Q: Let T3 be the Maclaurin polynomial of f(x) = e*. Use the Error Bound to find the maximum possible va...

A: