dx If S V(4+x?)3 = Sh(0) d0, then h(0) de %3D A 1 D 4 (B

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Q: d -(3x² + 11)e¬ª at x = –1. dx Evaluate

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Q: 3 d : 4me-m2 dy. dm

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Q: dy and d²y if x = t and y = 3. Find dx dx? 1+t 1+t

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Q: dy Q3) Find dx for 3(x? + y?) ² = 100xy

A: Here, the derivative dydx is obtained by implicit differentiation. Thus to find the derivative first…

Q: e substitution to evalua x+1 dx

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Q: 10 What is the value of S" F'(x) dx ?

A: Given,            y=Fx         We know that,        ∫abF'xdx=Fb-Fa

Q: dy Given y = x" In (2x), determine dx a.x“-' In (2x) + а-1 None

A: Please refer to the image below

Q: dx If |h(0) de, then h(e) d0 : (4+x²)³

A: Given, ∫dx4+x23=∫hθ dθ

Q: dx 1.5- 2x-x e if y = r(In x)² . . fr'e* dx. 2 if y = csch-1 20. de 2x+2 dx. -2x+1

A: since you have posted question with multiple subpart s, As per our guideline we supposed to answer…

Q: 까지 dx 10. A. In x + C B. In² [x] + C C. m² 1x1 xl 2 + + C

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Q: f (x) = [x + 4] df 1 =? dx 8 - O A) 1 В) 10 о с) -1 D) 2 O E) 0

A: The function f(x)=x+4. We have to find dfdx12=?

Q: S For x 1/2 x-x3 dx and using the substitutionu=x1/2

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Q: (d) S ! + de 1 d.x V1-x²

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Q: dx Find the value of if it exists. x2 – 1 1 8.

A: I=∫1∞dxx2-1=∫1∞dxx+1x-1=12∫1∞2dxx+1x-1=12∫1∞x+1-x-1x+1x-1

Q: 1 d) S e) S csc³x cot³x dx f) S dx x2Vx2 + 4 dx

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Q: (g) ſ 3e-(2=+7)dx (h) ſ 4xe(=²+3)dx ce(z (i) S(5e* + )dx

A: Integration of a function is an anti-derivative of that function, that is, if f(x) is the derivative…

Q: dy of x3 +v³ = 4 of X + dx Find O x? y² ,2

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Q: Find the value of E 2) Evaluate y dx 3) x e

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Q: S(-0) dx = - 4 In|x| + C 8. 2. )dx = 6 Vx + C

A: ∫x4-dx=x28-4ln(x)+CApply the Sum Rule:…

Q: S* (1– x)e* dx

A: To find out the integration.

Q: 2x dx x+x+7 S* r?e-3* dx

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Q: S- dx = In]x| – e* + C 5. S 2²+3*dx = 4| + C In 8

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Q: dy 10. y-x dx dx

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Q: S x2 (3u'le tlux-2) dx S12416 x3-2ye) dx Sle dut s l6 K3dx -S Zx? dx 5/2t1 シナリ こフv 341 7/2 구 /2 4…

A: Integration problem....

Q: e + d'x 2 dx dt + 5x = 8et when t-o, x -0 = 8

A: Please find the detailed solution in below images

Q: 3. = 9+y? xp. 3v4-x2 4. e' (5-x)dx = xydy dy _ (x+1)(y-2) 5. dx ху

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Q: In the function given. Evaluate the integrals.

A: ∫36-3gxdx=∫36-3dx·∫36gxdx Also, ∫36gxdx=1

Q: calculate the integral.

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Q: S(x-ae )Vx² + 2e" dx -ах - ах 11.

A: Let's find.

Q: € +h (1 g+ dy S

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Q: d?y Find for the given function. dx2 y = x - - - sin(x) 9 dzy dx2

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Q: dy at t = 2. dx If x = 5t +4 and y = 3t° -7, then find а. 4 b. 1 с. 2 d. 3

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Q: G + Kxy- 2x)dx + (3xy? +20x²y³)dy = 0

A: A differential equation (DE) of the form M(x,y) dx + N(x,y) dy = 0 is Exact iff ∂M∂y=∂N∂x Solution…

Q: dy Q3: Find an expression of for y = (x2)(Vx). dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dy You need not expand your answer. dx Calculate y = (7x2 + x)(x - x2) dy dx

A: Here a function y is given as a product of two functions . We have to find the derivative of the…

Q: dy If =-x+4x -3 and y =2 when x =0 then y is equal to dx

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Q: d The · (a²), where a is a constant, a e R, is dx A. 0

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Q: e2x -1 If y = In find dx dy e2x +1 ' Select the correct response: 2e2x e4x+1 e2x e 4x+1

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Q: (х + 3) e* - dx js equal to (x + 4)? 1 +c (x + 4)² et (x + 4)² x + 4 et x + 3

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Q: d²y - = 0 and dx? Let y=e" +b(x+1)'. When x = 0, that dx dy a) suppose = 0. Find the possible values…

A: Here we have to find the values of a and b. The solution is following .

Q: e-k* xn-1 dx ,n > 0 k> 0

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Q: Q.3 Solve (e* + 1)ydy = (y + 1)e*dx.

A: This is separable differential equation

Q: Q4 Find y'of y = ln- ? 1+e0 e

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Q: dx 3. S x V1-4 In2x

A: follow next step

Q: dx 4+e¬X A 4+e-* B C et (D) 4e*+1 E) None

A: ∫ ex/(4ex+1) dx

Q: Find dy/dx for the given value of x y = In(x² – 8) ; x=4 A. 1 В. 2 C. 0 D. 3 Е. 4

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Q: dy If y = (x- 1) e* then dx2 %3D O A.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: dy You need not expand your answer. dx Calculate 8.43x -0.1 0.5x-1 - 3.3 + x2.1

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Q: - S (x+1)dx в с х-1 (х-1)?, A If (x+2)(x– 1)² dx , the values of A & C respectively are + %3! x+2

A: The given equation is as follows. Solve the function by partial fractions as follows.

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.