15. Suppose X - Bino(2,). Find P(X = 0|X < 1). (а) 3/4 (b) 1/4 (c) 1/2 (d) 1/3 (е) 2/3

Q: d) f(x) = x* %3D

A:

Q: 13. (a) Find a number 8 such that if x- 2 < 8, then 4x - 8 < 8ɛ, where ɛ = 0.1. (b) Repeat part (a)…

A:

Q: 4. Show that 2y"-y'-y=0 when y=e* + e.

A:

Q: If f(x) In - In( + o). + e6x, find f (0).

A:

Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: 13. Calculate, where Som fx (w > fy (8-w) dw -16 окус). fx (x) = { 1 + 0xxx/ fyl2)= { 0, othmasid. !…

A: Given: fxx=1,0&lt;x&lt;10,otherwise   . . . (1)…

Q: 5. (x²-x)? 5.*- 5. - x2 – 2x + In|x|+C x3 2 6. S(6Vx – x-3)2 dx 6. 18x? + x3/2 8 1 + C 5x5

A:

Q: 6. y = xe* 7. y= 3x.e* 8. y = x² In(x) 9. y =x*(5x – 1) 10. y = (x² + 2x)5(3x-3 +x²)-7 11. y = (1 –…

A: Use product rule of differentiation.

Q: If P(XUY)=.P(X)= and P(X Y)= Find 7 P(X) b. P(Y) P(XnF) a. c.

A: Let A and B are two events then P(A U B) = P( A) + P(B) -P(A n B) Complement rule: P(A- ) = 1- P(A)…

Q: 25. h" (1), h(w)=√we"

A:

Q: (B) (AB) (BC) (CA) NY, 22.13. Show that if (A) (B) (C) = 3x and = x, 2x, %3D N N then the value of…

A:

Q: 24. Differentiate each of the following with respect to x. Simplify fully when indicated 1 (a)_y=x²³…

A:

Q: 5. Find y' for y=³√ 3√² + 3√/2

A: The given function is: y=3x2+53x As we know that, The Sum/Difference rule: f±g'=f'±g' The Power law:…

Q: 7. 7. Suppose X - N(u.4), which is true?( X- (A) N(0.1): (B) PIX S0} = 4 (C) PIX-u>2; =1-0(1): (D)…

A: Here we use the properties of normal distribution to solve this problem.

Q: (2 11) dx (x+2)* (x-1) *

A:

Q: 21 (a) ²x¹ d(x³). Note a(x) = x³. 3 (b) (²x² d(ex). Note a(x) = ex 2

A: Given :∫1213x4dx3∫24x2dex

Q: 1. D, [3x²y+In(xy²)] За + In(xg In(xy³)]

A: Given,

Q: 2 9. If f(x) =-(x- 5), determine the following %3D 3 f(17)- f(8) а) 17-8 (12)- f (4) b) 12 - 4

A: The given function    f(x)=23x-5

Q: 5. f() = {x? - 4 U x* -3 Evaluate f(4), f(0), f(-3) and f(-2/3) }" -2 if x = -3'

A: The objective is to evaluate f(4), f(0), f(-3) and f(-2/3).

Q: 1. Suppose that X ~ B(10, 0.12). Calculate: (b) P(X= 6) (е) Е(X) (а) Р(Х — 3) (d) P(X>7) (c) P(X<2)…

A: As per our guidelines we are suppose to answerthree sub parts.Given,A random variable X~B(10 ,…

Q: What is y' of y= 7√x 3√x ? A B C D 21√³ (In 7 + ln 3) (In 4) 21√x √x 21√ In 10 2√x 3 In ( - ) 21 V ²…

A: We have to find the point on paraboa y=-x2+4 whose tangent line is parallel with y=3x+5Parallel line…

Q: 10 6. Evaluate -dx. (x – 1)(x² + 9)*

A: Given integral is We will evaluate the integral by using the concept of partial fraction…

Q: Suppose f"(x) = N;(h) + a,h + azh² + azh³ + -…- ... The value of N2(h) using Richardson's…

A:

Q: If f(x) = 3x² +5+ (4x – 3)* | , then f '(x) is - + 5+ (4x – 3)*]" [4(4x – 3)'] B. [3* +5+ (4r -…

A: Given:            fx=3x2+5+4x-349 Solve: f'x           ddxfx=ddx3x2+5+4x-349

Q: 3 - dx x² – x - 2 (1) (ii) fx'e* dx

A:

Q: 9/Express flx) in the form fCx\=(x-K)q(x) tr for the given value o f k ):子メー5x3 -12x°-X; K3 -5 9.…

A:

Q: 7. If y = e*², then d²y dx2 boins9 (A) (2x)(x² – 1)e*²-2 stod beniu (B) ex2 (C) 2xe*2 (D) (2 +…

A:

Q: 1-2x (c) Determine the values of a, b and c if =1+ax+ bx? + cx. Hence, by 1+2x, 1 show that 2 s 3,…

A:

Q: · [2² 1. ² dx

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

Q: 33. (1 + r)' dr

A:

Q: 2/9 23. Evaluate dx. 11/9 11/9 81 x C) 119 A) +C 6- + C 11/9 9. B) 11 6- + C D) -9x+ C 18

A: This question is based on the substitution method.

Q: S₁ dx J2x (J2x +9)

A: To solve the given integral.

Q: (iv) 15-22 dr. u = (v) S 15 · T/9 – x² dx. 9-z (vi) J +15 da. u=

A: iv) 15x2/sqrt(9-x2) v) 15 pi sqrt(9-x2) vi) 9x/(x2+15).

Q: If y = (1 + x)(1 + x²)(1+x*)....(1 + x* ) then at x = 0 is - dx

A: Introduction :